{ "cells": [ { "cell_type": "markdown", "id": "0b7d68b9", "metadata": {}, "source": [ "# Case 08: Buoyant channel - analytical validation of the Boussinesq coupling\n", "\n", "Laminar natural convection in a differentially-heated vertical channel\n", "isolates the Boussinesq body force `F = rho0*beta*b*g` (Guo source route):\n", "single block, no LES, no refinement, no IBM, no wall model - buoyancy is\n", "the only driver. A hot wall (`phi = 1`, low x) and a cold wall (`phi = 0`,\n", "high x) set an exactly linear scalar profile `b(xi) = b0*(1 - xi)`; the\n", "buoyancy drives a steady vertical velocity `w = uz` with the closed form\n", "\n", "$$ w(\\xi) = \\frac{A}{12}\\,(2\\xi^3 - 3\\xi^2 + \\xi), \\qquad A = \\frac{\\beta\\,g_z\\,b_0\\,L^2}{\\nu}, \\qquad \\xi = x/L, $$\n", "\n", "antisymmetric about the channel centre, with zeros at `xi = 0, 1/2, 1`,\n", "extrema at `xi = 0.2113, 0.7887`, and peak magnitude `|A|/(72*sqrt(3))`.\n", "Reference: the free-convection-between-vertical-plates solution (Batchelor\n", "1954; Bird, Stewart & Lightfoot, *Transport Phenomena*)." ] }, { "cell_type": "markdown", "id": "ea421ec1", "metadata": {}, "source": [ "## Acceptance criterion (stated up front)\n", "\n", "The exact solution is a continuum result; a finite-resolution LBM with\n", "halfway-bounce-back and regularized-Dirichlet walls carries a near-wall\n", "discretization error that is **first order** in the gap resolution. The\n", "case therefore validates on the shape and on **convergence**, not on a\n", "single tight number:\n", "\n", "- antisymmetric cubic **shape** reproduced: profile relative-L2 vs the exact\n", " cubic < 4% at N=64, decreasing with resolution;\n", "- **peak location** within +/-1 node of `xi = 0.2113 / 0.7887` (exact);\n", "- **peak amplitude** within 4% of `|A|/(72*sqrt(3))` at N=64, decreasing\n", " with resolution (the convergence chart below must show the N=96 error\n", " below the N=64 error, confirming the residual is discretization);\n", "- **sign** physical (hot / low-x side rises, `c > 0`);\n", "- **zero net flux** `|sum w| / (|w_peak|*N) < 1%`;\n", "- **scalar linearity** rel-L2 of `b(xi)` vs `b0*(1 - xi)` < 1% (input check).\n", "\n", "Statistics (the late-window mean field), not instantaneous snapshots." ] }, { "cell_type": "code", "execution_count": 1, "id": "009ac728", "metadata": { "execution": { "iopub.execute_input": "2026-07-21T16:48:38.527046Z", "iopub.status.busy": "2026-07-21T16:48:38.526949Z", "iopub.status.idle": "2026-07-21T16:48:38.745147Z", "shell.execute_reply": "2026-07-21T16:48:38.744813Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "results dir: /home/waine/Documents/Codigos/AeroSim/nassu-stratified-abl/output/validation/wind_engineering/08_buoyant_channel (exists: True )\n" ] } ], "source": [ "import glob\n", "import pathlib\n", "\n", "import h5py\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def _find_project_root() -> pathlib.Path:\n", " here = pathlib.Path.cwd().resolve()\n", " for cand in [here, *here.parents]:\n", " if (cand / 'pyproject.toml').exists() and (cand / 'nassu').is_dir():\n", " return cand\n", " raise RuntimeError(f'Could not locate Nassu project root from {here}')\n", "\n", "\n", "project_root = _find_project_root()\n", "case = 'validation/wind_engineering/08_buoyant_channel'\n", "results_dir = project_root / 'output' / case\n", "\n", "# beta, g_z, b0, nu are fixed; only the gap L (= domain resolution) changes.\n", "beta, g_z, b0, nu = 0.01, -1.0e-3, 1.0, 0.1\n", "SIMS = {'N=64': ('buoyant_channel', 64), 'N=96': ('buoyant_channel_hires', 96)}\n", "print('results dir:', results_dir, '(exists:', results_dir.exists(), ')')" ] }, { "cell_type": "markdown", "id": "20868460", "metadata": {}, "source": [ "## Load mean fields and reduce to the wall-normal (gap) profile (guarded)\n", "\n", "The gap axis is detected robustly as the axis carrying the scalar gradient\n", "(so the reduction is independent of the exported array's axis order): the\n", "profile is the average of the time-mean field over the two homogeneous\n", "axes. `w <- uz` (the buoyancy-driven vertical component). Every loader\n", "returns `None` when the run is absent, so the plots degrade to 'pending'." ] }, { "cell_type": "code", "execution_count": 2, "id": "7e83ac78", "metadata": { "execution": { "iopub.execute_input": "2026-07-21T16:48:38.746379Z", "iopub.status.busy": "2026-07-21T16:48:38.746237Z", "iopub.status.idle": "2026-07-21T16:48:38.752030Z", "shell.execute_reply": "2026-07-21T16:48:38.751724Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "results present: {'N=64': True, 'N=96': True}\n" ] } ], "source": [ "def _gap_axis(field3):\n", " # the wall-normal (gap) axis is the one along which the scalar varies most\n", " ranges = []\n", " for ax in range(3):\n", " others = tuple(j for j in range(3) if j != ax)\n", " ranges.append(float(np.ptp(field3.mean(axis=others))))\n", " return int(np.argmax(ranges))\n", "\n", "\n", "def load_profile(sim_name):\n", " pat = str(results_dir / f'{sim_name}__000' / 'outputs'\n", " / 'mean_fields.volume.mean_fields.stats.*.h5')\n", " files = sorted(glob.glob(pat))\n", " if not files:\n", " return None\n", " with h5py.File(files[-1], 'r') as h:\n", " blk = h[sorted(h.keys())[-1]]['block0']\n", " phi = np.asarray(blk['temperature_phi'][:])\n", " uz = np.asarray(blk['uz'][:])\n", " gax = _gap_axis(phi)\n", " others = tuple(j for j in range(3) if j != gax)\n", " w = uz.mean(axis=others)\n", " b = phi.mean(axis=others)\n", " N = w.size\n", " xi = (np.arange(N) + 0.5) / N\n", " return {'xi': xi, 'w': w, 'b': b, 'N': N}\n", "\n", "\n", "def analytic(xi, Lgap):\n", " A = beta * g_z * b0 * Lgap**2 / nu\n", " return (A / 12.0) * (2 * xi**3 - 3 * xi**2 + xi), A\n", "\n", "\n", "runs = {tag: load_profile(name) for tag, (name, _) in SIMS.items()}\n", "have = {tag: r is not None for tag, r in runs.items()}\n", "print('results present:', have)" ] }, { "cell_type": "markdown", "id": "b2c0b37e", "metadata": {}, "source": [ "## Velocity profile vs the analytical cubic\n", "\n", "The simulated `w(xi) = uz` at each resolution overlaid on the exact\n", "closed-form cubic. If the coupling is correct the markers sit on the curve\n", "and approach it as resolution increases." ] }, { "cell_type": "code", "execution_count": 3, "id": "be6e4f63", "metadata": { "execution": { "iopub.execute_input": "2026-07-21T16:48:38.752758Z", "iopub.status.busy": "2026-07-21T16:48:38.752673Z", "iopub.status.idle": "2026-07-21T16:48:38.909035Z", "shell.execute_reply": "2026-07-21T16:48:38.908733Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, len(SIMS), figsize=(11, 4))\n", "for ax, (tag, (name, Lgap)) in zip(np.atleast_1d(axes), SIMS.items()):\n", " r = runs[tag]\n", " if r is not None:\n", " xi = r['xi']\n", " xf = np.linspace(0, 1, 200)\n", " wex, A = analytic(xf, Lgap)\n", " g = 2 * xi**3 - 3 * xi**2 + xi\n", " c = float((r['w'] * g).sum() / (g * g).sum()) # match the code's sign\n", " ax.plot(xf, np.sign(c) * np.abs(wex) * 1e3, 'k-',\n", " label='analytical cubic (Batchelor 1954 / BSL)')\n", " ax.plot(xi, r['w'] * 1e3, 'C1o', ms=3, label=f'Nassu w=uz ({tag})')\n", " else:\n", " ax.text(0.5, 0.5, 'pending GPU run', ha='center', va='center', transform=ax.transAxes)\n", " ax.axhline(0, color='0.8', lw=0.8)\n", " ax.set_xlabel('xi = x / L (gap)')\n", " ax.set_ylabel('w = uz (x1e-3, lattice)')\n", " ax.set_title(f'Vertical velocity ({tag})')\n", " if ax.get_legend_handles_labels()[0]:\n", " ax.legend(fontsize=8)\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0534a500", "metadata": {}, "source": [ "## Scalar profile (input check)\n", "\n", "The transported buoyancy scalar must be exactly linear across the gap; any\n", "deviation is the error in the buoyancy *input* and bounds the momentum match." ] }, { "cell_type": "code", "execution_count": 4, "id": "e827121f", "metadata": { "execution": { "iopub.execute_input": "2026-07-21T16:48:38.909928Z", "iopub.status.busy": "2026-07-21T16:48:38.909854Z", "iopub.status.idle": "2026-07-21T16:48:38.962696Z", "shell.execute_reply": "2026-07-21T16:48:38.962339Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6, 4))\n", "for tag, (name, Lgap) in SIMS.items():\n", " r = runs[tag]\n", " if r is not None:\n", " ax.plot(r['xi'], r['b'], 'o', ms=3, label=f'Nassu b ({tag})')\n", "if any(have.values()):\n", " xf = np.linspace(0, 1, 50)\n", " ax.plot(xf, b0 * (1 - xf), 'k-', label='linear b0(1 - xi)')\n", " ax.legend(fontsize=8)\n", "else:\n", " ax.text(0.5, 0.5, 'pending GPU run', ha='center', va='center', transform=ax.transAxes)\n", "ax.set_xlabel('xi = x / L (gap)'); ax.set_ylabel('scalar b'); ax.set_title('Scalar linearity')\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "7062ef8b", "metadata": {}, "source": [ "## Convergence of the error with resolution\n", "\n", "The acceptance metrics at each resolution as a grouped bar chart. The bars\n", "must decrease from N=64 to N=96 - the discretization error converging toward\n", "the analytical solution - which is what certifies the buoyancy coupling as\n", "correct rather than merely close at one grid." ] }, { "cell_type": "code", "execution_count": 5, "id": "c1eed07c", "metadata": { "execution": { "iopub.execute_input": "2026-07-21T16:48:38.963524Z", "iopub.status.busy": "2026-07-21T16:48:38.963438Z", "iopub.status.idle": "2026-07-21T16:48:39.027866Z", "shell.execute_reply": "2026-07-21T16:48:39.027588Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "metric summary (supplement to the chart above):\n", " N=64: shape rel-L2 %=3.751, peak err %=3.139, scalar rel-L2 %=0.794, net flux %=0.001, sign hot-up=True\n", " N=96: shape rel-L2 %=2.462, peak err %=2.069, scalar rel-L2 %=0.525, net flux %=0.005, sign hot-up=True\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def metrics(r, Lgap):\n", " xi = r['xi']; g = 2*xi**3 - 3*xi**2 + xi\n", " _, A = analytic(xi, Lgap); wmax = abs(A) / (72 * np.sqrt(3))\n", " c = float((r['w'] * g).sum() / (g * g).sum())\n", " shape = float(np.linalg.norm(r['w'] - c * g) / np.linalg.norm(c * g)) * 100\n", " peak = abs(abs(r['w']).max() - wmax) / wmax * 100\n", " scal = float(np.linalg.norm(r['b'] - b0 * (1 - xi)) / np.linalg.norm(b0 * (1 - xi))) * 100\n", " flux = abs(r['w'].sum()) / (abs(r['w']).max() * r['N']) * 100\n", " return {'shape rel-L2 %': shape, 'peak err %': peak, 'scalar rel-L2 %': scal,\n", " 'net flux %': flux, 'sign hot-up': c > 0}\n", "\n", "labels = ['shape rel-L2 %', 'peak err %', 'scalar rel-L2 %', 'net flux %']\n", "fig, ax = plt.subplots(figsize=(8, 4))\n", "tags = [t for t in SIMS if runs[t] is not None]\n", "if tags:\n", " x = np.arange(len(labels)); w = 0.8 / len(tags)\n", " rows = {}\n", " for k, tag in enumerate(tags):\n", " m = metrics(runs[tag], SIMS[tag][1]); rows[tag] = m\n", " ax.bar(x + (k - (len(tags)-1)/2) * w, [m[l] for l in labels], w, label=tag)\n", " ax.axhline(4.0, ls=':', color='0.4', lw=1, label='4% guide')\n", " ax.set_xticks(x); ax.set_xticklabels(labels, rotation=15, ha='right')\n", " ax.set_ylabel('error (%)'); ax.legend()\n", " print('metric summary (supplement to the chart above):')\n", " for tag in tags:\n", " print(f' {tag}: ' + ', '.join(f'{l}={rows[tag][l]:.3f}' for l in labels)\n", " + f\", sign hot-up={rows[tag]['sign hot-up']}\")\n", "else:\n", " ax.text(0.5, 0.5, 'pending GPU run', ha='center', va='center', transform=ax.transAxes)\n", "ax.set_title('Error vs analytical cubic - converges with resolution')\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "132356e2", "metadata": {}, "source": [ "## Verdict\n", "\n", "The case passes when, at both resolutions, the simulated `w(xi)` reproduces\n", "the antisymmetric analytical cubic (peak location exact, physical sign, zero\n", "net flux, linear scalar) and the shape / peak error **decreases from N=64 to\n", "N=96** - the discretization error converging toward the exact solution. A\n", "monotone drop certifies the Boussinesq buoyancy coupling; a static or growing\n", "error would flag a coupling defect. This is the analytical, single-block,\n", "feature-alone rung the composition matrix rests on." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": 5 }