{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poiseuille Channel (Multilevel)\n",
    "\n",
    "In this simulation, the multilevel approach is tested to check the macroscopics continuity when passing through different levels and when applied at boundary regions of the computational domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:42.757912Z",
     "iopub.status.busy": "2026-06-29T17:41:42.757812Z",
     "iopub.status.idle": "2026-06-29T17:41:43.225708Z",
     "shell.execute_reply": "2026-06-29T17:41:43.225325Z"
    }
   },
   "outputs": [],
   "source": [
    "from nassu.cfg.model import ConfigScheme\n",
    "\n",
    "filename = \"validation/analytical/02_poiseuille_channel_flow/02_poiseuille_channel_flow.nassu.yaml\"\n",
    "\n",
    "sim_cfgs = ConfigScheme.sim_cfgs_from_file_dct(filename)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, a small value for the relaxation time $\\tau$ was adopted. Since the aim is to check possible discontinuities in the multilevel formulation, less stable values of $\\tau$ could highlight implementation issues."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:43.226856Z",
     "iopub.status.busy": "2026-06-29T17:41:43.226722Z",
     "iopub.status.idle": "2026-06-29T17:41:43.228305Z",
     "shell.execute_reply": "2026-06-29T17:41:43.228091Z"
    }
   },
   "outputs": [],
   "source": [
    "sim_cfg = next(\n",
    "    sim_cfg\n",
    "    for (name, _), sim_cfg in sim_cfgs.items()\n",
    "    if name == \"velocityNeumannPoiseuilleChannelMultilevel\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract data from multiblock data from output file of macrs export"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:43.229039Z",
     "iopub.status.busy": "2026-06-29T17:41:43.228968Z",
     "iopub.status.idle": "2026-06-29T17:41:43.854480Z",
     "shell.execute_reply": "2026-06-29T17:41:43.854149Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys([(0, 'velocityNeumannPoiseuilleChannelMultilevel')])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from vtkmodules.util.numpy_support import vtk_to_numpy\n",
    "\n",
    "import nassu.viz as common\n",
    "\n",
    "common.use_style()\n",
    "\n",
    "extracted_data = {}\n",
    "array_to_extract = \"ux\"\n",
    "\n",
    "export_instantaneous_cfg = sim_cfg.output.exports\n",
    "macr_export = export_instantaneous_cfg[\"default\"].volumes[\"default\"].inst\n",
    "time_step = macr_export.time_steps(sim_cfg.n_steps)[-1]\n",
    "data = macr_export.read_export(time_step)\n",
    "\n",
    "p1 = [sim_cfg.domain.domain_size.x * 0.75, 0.5, 0]\n",
    "p2 = [sim_cfg.domain.domain_size.x * 0.75, sim_cfg.domain.domain_size.y - 0.5, 0]\n",
    "line = common.create_line(p1, p2, sim_cfg.domain.domain_size.y - 1)\n",
    "\n",
    "pos = np.linspace(p1, p2, sim_cfg.domain.domain_size.y)\n",
    "\n",
    "probe_filter = common.probe_over_line(line, data)\n",
    "\n",
    "probed_data = vtk_to_numpy(probe_filter.GetOutput().GetPointData().GetArray(array_to_extract))\n",
    "extracted_data[(sim_cfg.sim_id, sim_cfg.name)] = {\"pos\": pos, \"data\": probed_data}\n",
    "\n",
    "extracted_data.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract data from multiblock data from output file of macrs export for rho plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:43.871819Z",
     "iopub.status.busy": "2026-06-29T17:41:43.871593Z",
     "iopub.status.idle": "2026-06-29T17:41:43.955918Z",
     "shell.execute_reply": "2026-06-29T17:41:43.955600Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, 'velocityNeumannPoiseuilleChannelMultilevel', 0): np.float32(1.0),\n",
       " (0,\n",
       "  'velocityNeumannPoiseuilleChannelMultilevel',\n",
       "  12000): np.float32(1.0145637),\n",
       " (0,\n",
       "  'velocityNeumannPoiseuilleChannelMultilevel',\n",
       "  24000): np.float32(1.0145637),\n",
       " (0,\n",
       "  'velocityNeumannPoiseuilleChannelMultilevel',\n",
       "  36000): np.float32(1.0145637),\n",
       " (0,\n",
       "  'velocityNeumannPoiseuilleChannelMultilevel',\n",
       "  48000): np.float32(1.0145637),\n",
       " (0,\n",
       "  'velocityNeumannPoiseuilleChannelMultilevel',\n",
       "  60000): np.float32(1.0145637)}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_data = {}\n",
    "array_to_extract = \"rho\"\n",
    "\n",
    "for time_step in macr_export.interval.get_all_process_steps(sim_cfg.n_steps):\n",
    "    reader = macr_export.read_xdmf_export(time_step)\n",
    "\n",
    "    multiblock_dataset = reader.GetOutput()\n",
    "    n_blocks = multiblock_dataset.GetNumberOfBlocks()\n",
    "\n",
    "    blocks_data = []\n",
    "    for i in range(n_blocks):\n",
    "        block = multiblock_dataset.GetBlock(i)\n",
    "        data_array = vtk_to_numpy(block.GetCellData().GetArray(array_to_extract))\n",
    "        blocks_data.append(data_array)\n",
    "    multiblock_avg = np.average(np.concatenate(blocks_data).flatten())\n",
    "\n",
    "    average_data[(sim_cfg.sim_id, sim_cfg.name, time_step)] = multiblock_avg\n",
    "\n",
    "average_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract data from multiblock data from output file of macrs export for profile plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:43.956847Z",
     "iopub.status.busy": "2026-06-29T17:41:43.956776Z",
     "iopub.status.idle": "2026-06-29T17:41:43.973227Z",
     "shell.execute_reply": "2026-06-29T17:41:43.972927Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys([(0, 'velocityNeumannPoiseuilleChannelMultilevel')])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "profile_data = {}\n",
    "array_to_extract = \"ux\"\n",
    "\n",
    "time_step = macr_export.time_steps(sim_cfg.n_steps)[-1]\n",
    "data = macr_export.read_export(time_step)\n",
    "\n",
    "p1 = [0.25, sim_cfg.domain.domain_size.y / 2, 0]\n",
    "p2 = [sim_cfg.domain.domain_size.x - 0.25, sim_cfg.domain.domain_size.y / 2, 0]\n",
    "line = common.create_line(p1, p2, 2 * sim_cfg.domain.domain_size.x - 1)\n",
    "\n",
    "pos = np.linspace(p1, p2, sim_cfg.domain.domain_size.x * 2)\n",
    "\n",
    "probe_filter = common.probe_over_line(line, data)\n",
    "\n",
    "probed_data = vtk_to_numpy(probe_filter.GetOutput().GetPointData().GetArray(array_to_extract))\n",
    "profile_data[(sim_cfg.sim_id, sim_cfg.name)] = {\"pos\": np.array(pos), \"data\": probed_data}\n",
    "\n",
    "profile_data.keys()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "The velocity profile at the end of simulation is compared with the steady state analytical solution below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Processing functions for Poiseuille Flow case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:43.974183Z",
     "iopub.status.busy": "2026-06-29T17:41:43.974100Z",
     "iopub.status.idle": "2026-06-29T17:41:43.975953Z",
     "shell.execute_reply": "2026-06-29T17:41:43.975722Z"
    }
   },
   "outputs": [],
   "source": [
    "from typing import Callable\n",
    "\n",
    "\n",
    "def get_poiseuille_analytical_func() -> Callable:\n",
    "    \"\"\"Poiseuille analytical velocity function\n",
    "\n",
    "    Returns:\n",
    "        Callable: Analytical velocity function\n",
    "    \"\"\"\n",
    "    return lambda pos: 6 * (pos - pos**2)\n",
    "\n",
    "\n",
    "def plot_analytical_poiseuille_vels(ax):\n",
    "    x = np.arange(0, 1.01, 0.01)\n",
    "    analytical_func = get_poiseuille_analytical_func()\n",
    "    analytical_data = analytical_func(x)\n",
    "    ax.plot(x, analytical_data, **common.markers.exp_line(linestyle=\"--\"), label=\"Analytical\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:43.976614Z",
     "iopub.status.busy": "2026-06-29T17:41:43.976549Z",
     "iopub.status.idle": "2026-06-29T17:41:44.064197Z",
     "shell.execute_reply": "2026-06-29T17:41:44.063837Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = common.fig_single()\n",
    "\n",
    "num_data = extracted_data[(sim_cfg.sim_id, sim_cfg.name)]\n",
    "num_avg_vel = np.average(num_data[\"data\"])\n",
    "position_vector = (num_data[\"pos\"][:, 1] - 0.5) / (sim_cfg.domain.domain_size.y - 1)\n",
    "ax.plot(\n",
    "    position_vector,\n",
    "    num_data[\"data\"] / num_avg_vel,\n",
    "    **common.markers.sim(shape=\"o\", alpha=0.8),\n",
    "    label=f\"N={sim_cfg.domain.domain_size.x} (avg. {num_avg_vel:.2e})\",\n",
    ")\n",
    "\n",
    "plot_analytical_poiseuille_vels(ax)\n",
    "ax.set_title(\n",
    "    f\"Poiseuille (Multilevel)\\n({sim_cfg.models.LBM.vel_set} {sim_cfg.models.LBM.coll_oper})\"\n",
    ")\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show(fig)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No discontinuities issues are seen through the velocity profile, indicating a satisfactory implementation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:44.065082Z",
     "iopub.status.busy": "2026-06-29T17:41:44.065009Z",
     "iopub.status.idle": "2026-06-29T17:41:44.112074Z",
     "shell.execute_reply": "2026-06-29T17:41:44.111759Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = common.fig_single()\n",
    "\n",
    "plotting_data: list[float] = []\n",
    "axis_data: list[int] = []\n",
    "\n",
    "for (_, _, timestep), average_val in average_data.items():\n",
    "    plotting_data.append(average_val)\n",
    "    axis_data.append(timestep)\n",
    "\n",
    "ax.plot(\n",
    "    axis_data, plotting_data, **common.markers.sim(shape=\"o\"), label=f\"Average {array_to_extract}\"\n",
    ")\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show(fig)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average pressure sustains the convergence aspect exhibited in the single level simulation, though it takes longer to converge since a smaller value of $\\tau$ was adopted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:44.112989Z",
     "iopub.status.busy": "2026-06-29T17:41:44.112893Z",
     "iopub.status.idle": "2026-06-29T17:41:44.320224Z",
     "shell.execute_reply": "2026-06-29T17:41:44.319943Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[0m\u001b[33m2026-06-29 14:41:44.136 (   0.898s) [    7F6F97F23740]vtkXOpenGLRenderWindow.:1460  WARN| bad X server connection. DISPLAY=\u001b[0m\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pyvista as pv\n",
    "\n",
    "array_to_inspect = \"rho\"\n",
    "\n",
    "plotter = pv.Plotter(window_size=(800, 400))\n",
    "\n",
    "time_step = macr_export.time_steps(sim_cfg.n_steps)[-1]\n",
    "xdmf_reader = pv.get_reader(str(macr_export.xdmf_filename))\n",
    "xdmf_reader.set_active_time_value(float(time_step))\n",
    "mesh = xdmf_reader.read()\n",
    "mesh.set_active_scalars(array_to_inspect)\n",
    "plotter.add_mesh(mesh, cmap=\"coolwarm\")\n",
    "\n",
    "plot_title = (\n",
    "    f\"{array_to_inspect} profile Poiseuille (Multilevel)\\n\"\n",
    "    f\"({sim_cfg.models.LBM.vel_set} {sim_cfg.models.LBM.coll_oper})\"\n",
    ")\n",
    "plotter.add_text(plot_title, position=\"upper_right\", font_size=18, color=\"black\")\n",
    "plotter.camera_position = [(48.0, 12.0, -192.16548199848856), (48.0, 12.0, 1.0), (0.0, -1.0, 0.0)]\n",
    "plotter.camera.zoom(2)\n",
    "plotter.show(jupyter_backend=\"static\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general flow's density profile shown above presents no visible disconuity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:44.321172Z",
     "iopub.status.busy": "2026-06-29T17:41:44.321099Z",
     "iopub.status.idle": "2026-06-29T17:41:44.371776Z",
     "shell.execute_reply": "2026-06-29T17:41:44.371452Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = common.fig_single()\n",
    "\n",
    "num_data = profile_data[(sim_cfg.sim_id, sim_cfg.name)]\n",
    "position_vector = (num_data[\"pos\"][:, 0] - 0.5) / (sim_cfg.domain.domain_size.x - 1)\n",
    "ax.plot(position_vector, num_data[\"data\"], **common.markers.sim_line())\n",
    "\n",
    "ax.set_title(\n",
    "    f\"Ux profile Poiseuille (Multilevel)\\n({sim_cfg.models.LBM.vel_set} {sim_cfg.models.LBM.coll_oper})\"\n",
    ")\n",
    "plt.tight_layout()\n",
    "plt.show(fig)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The centerline velocity has an asympotic profile. However, it would take a longer length for the velocity to completely stabilizes.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:44.372691Z",
     "iopub.status.busy": "2026-06-29T17:41:44.372612Z",
     "iopub.status.idle": "2026-06-29T17:41:44.414757Z",
     "shell.execute_reply": "2026-06-29T17:41:44.414534Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Version:"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0.1a0"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Commit hash:"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20647b9f11c91d10aafe36bf0a564a3a38f9d08a"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "sim_info = sim_cfg.output.read_info()\n",
    "\n",
    "nassu_commit = sim_info[\"commit\"]\n",
    "nassu_version = sim_info[\"version\"]\n",
    "print(\"Version:\", nassu_version)\n",
    "print(\"Commit hash:\", nassu_commit)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:41:44.415730Z",
     "iopub.status.busy": "2026-06-29T17:41:44.415642Z",
     "iopub.status.idle": "2026-06-29T17:41:44.452729Z",
     "shell.execute_reply": "2026-06-29T17:41:44.452445Z"
    }
   },
   "outputs": [
    {
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       ".output_html .il { color: #666 } /* Literal.Number.Integer.Long */</style><div class=\"highlight\"><pre><span></span><span class=\"nt\">simulations</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">periodicPoiseuilleChannel</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">save_path</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/analytical/02_poiseuille_channel_flow/results/periodic</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">n_steps</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">250</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">4000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16000</span><span class=\"p p-Indicator\">]</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">report</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1000</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">domain</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">domain_size</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">x</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">4</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">32</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">y</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">4</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">32</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">block_size</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">4</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">]</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">data</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">exports</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">macrs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">rho</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">u</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">interval</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">target</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">volume</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">outputs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">instantaneous</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">models</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">precision</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">single</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">LBM</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">tau</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.9</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">vel_set</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">D2Q9</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">coll_oper</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RRBGK</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">F</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"c1\"># FX is divided by 8</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">x</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">4.0e-4</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">5.0e-5</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">6.25e-6</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">7.8125e-07</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">y</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">multiblock</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">overlap_F2C</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">engine</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">CUDA</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">BC</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">periodic_dims</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">true</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">false</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">BC_map</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">HWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">HWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "\n",
       "<span class=\"w\">  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">regularizedPeriodicPoiseuilleChannel</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">parent</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">periodicPoiseuilleChannel</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">models</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">LBM</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">coll_oper</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RRBGK</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">BC</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">periodic_dims</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">true</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">false</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">BC_map</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "\n",
       "<span class=\"w\">  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">velocityNeumannPoiseuilleChannel</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">parent</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">periodicPoiseuilleChannel</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">save_path</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/analytical/02_poiseuille_channel_flow/results/velocity_neumann</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">report</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1000</span><span class=\"p p-Indicator\">}</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">n_steps</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">64000</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">domain</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">domain_size</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">x</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">256</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">y</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">32</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">block_size</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">8</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">data</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">exports</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">macrs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">rho</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">u</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">interval</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">16000</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">target</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">volume</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">outputs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">instantaneous</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">models</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">LBM</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!not-inherit</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">tau</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.9</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">vel_set</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">D2Q9</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">coll_oper</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RRBGK</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">BC</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">periodic_dims</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">false</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">false</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">BC_map</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">UniformFlow</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">ux</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.05</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">uy</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">uz</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedNeumannOutlet</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "\n",
       "<span class=\"w\">  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">velocityNeumannPoiseuilleChannelMultilevel</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">parent</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">periodicPoiseuilleChannel</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">save_path</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/analytical/02_poiseuille_channel_flow/results/multilevel</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">n_steps</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">64000</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">domain</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">domain_size</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">x</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">96</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">y</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">24</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">block_size</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">8</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">refinement</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">static</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">default</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">volumes_refine</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">24</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">8</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">24</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">16</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">32</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">24</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">48</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">24</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">40</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">48</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">56</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">72</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">80</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">88</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">88</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">96</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">24</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">}</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">data</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">exports</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">macrs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">rho</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">u</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">S</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">interval</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">12000</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">target</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">volume</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">outputs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">instantaneous</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">models</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">precision</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">single</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">LBM</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!not-inherit</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">tau</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.8</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">vel_set</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">D2Q9</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">coll_oper</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RRBGK</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">engine</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">CUDA</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">BC</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">periodic_dims</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">false</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">false</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">BC_map</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">UniformFlow</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">ux</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.05</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">uy</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">uz</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedNeumannOutlet</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">N</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">S</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "</pre></div>\n"
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       "\\PY{+w}{          }\\PY{n+nt}{interval}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{frequency}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{12000}\n",
       "\\PY{+w}{            }\\PY{n+nt}{lvl}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
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       "\n",
       "\\PY{+w}{    }\\PY{n+nt}{models}\\PY{p}{:}\n",
       "\\PY{+w}{      }\\PY{n+nt}{precision}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{default}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{single}\n",
       "\n",
       "\\PY{+w}{      }\\PY{n+nt}{LBM}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!not\\PYZhy{}inherit}\n",
       "\\PY{+w}{        }\\PY{n+nt}{tau}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.8}\n",
       "\\PY{+w}{        }\\PY{n+nt}{vel\\PYZus{}set}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{D2Q9}\n",
       "\\PY{+w}{        }\\PY{n+nt}{coll\\PYZus{}oper}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{RRBGK}\n",
       "\n",
       "\\PY{+w}{      }\\PY{n+nt}{engine}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{name}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{CUDA}\n",
       "\n",
       "\\PY{+w}{      }\\PY{n+nt}{BC}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{periodic\\PYZus{}dims}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{false}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{false}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{true}\\PY{p+pIndicator}{]}\n",
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       "\\PY{+w}{            }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{UniformFlow}\n",
       "\\PY{+w}{            }\\PY{n+nt}{rho}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1.0}\n",
       "\\PY{+w}{            }\\PY{n+nt}{ux}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.05}\n",
       "\\PY{+w}{            }\\PY{n+nt}{uy}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\PY{+w}{            }\\PY{n+nt}{uz}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\PY{+w}{            }\\PY{n+nt}{order}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1}\n",
       "\n",
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       "\\PY{+w}{            }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{RegularizedNeumannOutlet}\n",
       "\\PY{+w}{            }\\PY{n+nt}{rho}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1.0}\n",
       "\\PY{+w}{            }\\PY{n+nt}{wall\\PYZus{}normal}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{E}\n",
       "\\PY{+w}{            }\\PY{n+nt}{order}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1}\n",
       "\n",
       "\\PY{+w}{          }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{n+nt}{pos}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{N}\n",
       "\\PY{+w}{            }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{RegularizedHWBB}\n",
       "\\PY{+w}{            }\\PY{n+nt}{wall\\PYZus{}normal}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{N}\n",
       "\\PY{+w}{            }\\PY{n+nt}{order}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\n",
       "\\PY{+w}{          }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{n+nt}{pos}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{S}\n",
       "\\PY{+w}{            }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{RegularizedHWBB}\n",
       "\\PY{+w}{            }\\PY{n+nt}{wall\\PYZus{}normal}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{S}\n",
       "\\PY{+w}{            }\\PY{n+nt}{order}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\end{Verbatim}\n"
      ],
      "text/plain": [
       "simulations:\n",
       "  - name: periodicPoiseuilleChannel\n",
       "    save_path: ./validation/analytical/02_poiseuille_channel_flow/results/periodic\n",
       "\n",
       "    n_steps: !unroll [250, 1000, 4000, 16000]\n",
       "\n",
       "    report:\n",
       "      frequency: 1000\n",
       "\n",
       "    domain:\n",
       "      domain_size:\n",
       "        x: !unroll [4, 8, 16, 32]\n",
       "        y: !unroll [4, 8, 16, 32]\n",
       "      block_size: !unroll [4, 8, 8, 8]\n",
       "\n",
       "    data:\n",
       "      exports:\n",
       "        default:\n",
       "          macrs: [rho, u]\n",
       "          interval:\n",
       "            frequency: 0\n",
       "            lvl: 0\n",
       "          target:\n",
       "            volume: {}\n",
       "          outputs:\n",
       "            instantaneous: true\n",
       "\n",
       "    models:\n",
       "      precision:\n",
       "        default: single\n",
       "\n",
       "      LBM:\n",
       "        tau: 0.9\n",
       "        vel_set: D2Q9\n",
       "        coll_oper: RRBGK\n",
       "        F:\n",
       "          # FX is divided by 8\n",
       "          x: !unroll [4.0e-4, 5.0e-5, 6.25e-6, 7.8125e-07]\n",
       "          y: 0\n",
       "\n",
       "      multiblock:\n",
       "        overlap_F2C: 1\n",
       "\n",
       "      engine:\n",
       "        name: CUDA\n",
       "\n",
       "      BC:\n",
       "        periodic_dims: [true, false]\n",
       "        BC_map:\n",
       "          - pos: N\n",
       "            BC: HWBB\n",
       "            wall_normal: N\n",
       "\n",
       "          - pos: S\n",
       "            BC: HWBB\n",
       "            wall_normal: S\n",
       "\n",
       "  - name: regularizedPeriodicPoiseuilleChannel\n",
       "    parent: periodicPoiseuilleChannel\n",
       "\n",
       "    models:\n",
       "      LBM:\n",
       "        coll_oper: RRBGK\n",
       "\n",
       "      BC:\n",
       "        periodic_dims: [true, false]\n",
       "        BC_map:\n",
       "          - pos: N\n",
       "            BC: RegularizedHWBB\n",
       "            wall_normal: N\n",
       "\n",
       "          - pos: S\n",
       "            BC: RegularizedHWBB\n",
       "            wall_normal: S\n",
       "\n",
       "  - name: velocityNeumannPoiseuilleChannel\n",
       "    parent: periodicPoiseuilleChannel\n",
       "\n",
       "    save_path: ./validation/analytical/02_poiseuille_channel_flow/results/velocity_neumann\n",
       "\n",
       "    report: {frequency: 1000}\n",
       "\n",
       "    n_steps: 64000\n",
       "    domain:\n",
       "      domain_size:\n",
       "        x: 256\n",
       "        y: 32\n",
       "      block_size: 8\n",
       "\n",
       "    data:\n",
       "      exports:\n",
       "        default:\n",
       "          macrs: [rho, u]\n",
       "          interval:\n",
       "            frequency: 16000\n",
       "            lvl: 0\n",
       "          target:\n",
       "            volume: {}\n",
       "          outputs:\n",
       "            instantaneous: true\n",
       "\n",
       "    models:\n",
       "      LBM: !not-inherit\n",
       "        tau: 0.9\n",
       "        vel_set: D2Q9\n",
       "        coll_oper: RRBGK\n",
       "\n",
       "      BC:\n",
       "        periodic_dims: [false, false]\n",
       "        BC_map:\n",
       "          - pos: W\n",
       "            BC: UniformFlow\n",
       "            wall_normal: W\n",
       "            rho: 1.0\n",
       "            ux: 0.05\n",
       "            uy: 0\n",
       "            uz: 0\n",
       "            order: 1\n",
       "\n",
       "          - pos: E\n",
       "            BC: RegularizedNeumannOutlet\n",
       "            rho: 1.0\n",
       "            wall_normal: E\n",
       "            order: 1\n",
       "\n",
       "          - pos: N\n",
       "            BC: RegularizedHWBB\n",
       "            wall_normal: N\n",
       "            order: 0\n",
       "\n",
       "          - pos: S\n",
       "            BC: RegularizedHWBB\n",
       "            wall_normal: S\n",
       "            order: 0\n",
       "\n",
       "  - name: velocityNeumannPoiseuilleChannelMultilevel\n",
       "    parent: periodicPoiseuilleChannel\n",
       "\n",
       "    save_path: ./validation/analytical/02_poiseuille_channel_flow/results/multilevel\n",
       "\n",
       "    n_steps: 64000\n",
       "\n",
       "    domain:\n",
       "      domain_size:\n",
       "        x: 96\n",
       "        y: 24\n",
       "      block_size: 8\n",
       "      refinement:\n",
       "        static:\n",
       "          default:\n",
       "            volumes_refine:\n",
       "              - {start: [0, 0], end: [8, 8], lvl: 1, is_abs: true}\n",
       "              - {start: [0, 16], end: [8, 24], lvl: 1, is_abs: true}\n",
       "              - {start: [8, 8], end: [24, 16], lvl: 1, is_abs: true}\n",
       "              - {start: [16, 0], end: [32, 8], lvl: 1, is_abs: true}\n",
       "              - {start: [24, 16], end: [48, 24], lvl: 1, is_abs: true}\n",
       "              - {start: [40, 8], end: [48, 16], lvl: 1, is_abs: true}\n",
       "              - {start: [56, 0], end: [72, 8], lvl: 1, is_abs: true}\n",
       "              - {start: [80, 8], end: [88, 16], lvl: 1, is_abs: true}\n",
       "              - {start: [88, 16], end: [96, 24], lvl: 1, is_abs: true}\n",
       "\n",
       "    data:\n",
       "      exports:\n",
       "        default:\n",
       "          macrs: [rho, u, S]\n",
       "          interval:\n",
       "            frequency: 12000\n",
       "            lvl: 0\n",
       "          target:\n",
       "            volume: {}\n",
       "          outputs:\n",
       "            instantaneous: true\n",
       "\n",
       "    models:\n",
       "      precision:\n",
       "        default: single\n",
       "\n",
       "      LBM: !not-inherit\n",
       "        tau: 0.8\n",
       "        vel_set: D2Q9\n",
       "        coll_oper: RRBGK\n",
       "\n",
       "      engine:\n",
       "        name: CUDA\n",
       "\n",
       "      BC:\n",
       "        periodic_dims: [false, false, true]\n",
       "        BC_map:\n",
       "          - pos: W\n",
       "            BC: UniformFlow\n",
       "            rho: 1.0\n",
       "            ux: 0.05\n",
       "            uy: 0\n",
       "            uz: 0\n",
       "            order: 1\n",
       "\n",
       "          - pos: E\n",
       "            BC: RegularizedNeumannOutlet\n",
       "            rho: 1.0\n",
       "            wall_normal: E\n",
       "            order: 1\n",
       "\n",
       "          - pos: N\n",
       "            BC: RegularizedHWBB\n",
       "            wall_normal: N\n",
       "            order: 0\n",
       "\n",
       "          - pos: S\n",
       "            BC: RegularizedHWBB\n",
       "            wall_normal: S\n",
       "            order: 0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Code\n",
    "\n",
    "Code(filename=filename)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "nassu (3.12.13)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}