Buildings Area Density: 0.1
***************************

.. html metadata
.. meta::
   :description: Flat-roofed Surrounded Building - Buildings Area Density: 0.1
   :keywords: Digital Wind Tunnel, Validation, Flat-roofed Surrounded Building, Buildings Area Density: 0.1

.. Public Project
.. ==============
.. .. link to insight page
.. `AeroSim Web App`_

.. .. _AeroSim Web App: https://insight.aerosim.io/cp/TODEFINE/


.. animations, surfaces and contours
.. figure_expand:: /_static/neighbour/c_01/visuals_1.png
   :alt: Buildings Area Density: 0.1
   :figwidth: 100%
   :align: center

1. Project Description
======================

The current study numerically reproduces the experiment `103213`_ from the Tokyo Polytechnic University (TPU) Aerodynamic Database with AeroSim's CFD solver.

A low-rise building with :math:`B \times W \times H` dimensions:

.. _103213: https://db.wind.arch.t-kougei.ac.jp/aerodynamic/case/103213/ 
.. Cite experimental database or paper

.. Comprehensive description of the geometries and dimensions
.. figure_expand:: /_static/neighbour/geometry.svg
   :alt: Building Geometry
   :max-width: 640px
   :align: center

is positioned in a wind tunnel setup with 184 pressure probes distributed over its surface:

.. Probes location and wind direction orientation
.. figure_expand:: /_static/neighbour/probes.svg
   :alt: Probes Layout
   :max-width: 640px
   :align: center

The target model was positioned at the center of a turnable of 200m diameter, in full scale, with the surrounding buildings regularly arranged within its radius:

.. Probes location and wind direction orientation
.. figure_expand:: /_static/neighbour/c_01/surroundings.svg
   :alt: Buildings Layout
   :max-width: 640px
   :align: center

To which the density of buildings is determined by an area density coefficient 

.. math:: 
  \mathrm{C_{A}}=\mathrm{\frac{area\,occupied\,by\,the\,buildings}{area\,of\,site}}=\frac{BW}{D_{1}D_{2}}

Which for the current case is :math:`\mathrm{C_{A}}=0.1`.

The wind directions chosen to be simulated were:

.. list of analyzed cases
.. csv-table:: Wind Directions
   :file: /_static/neighbour/c_01/cases.csv
   :widths: 16, 16, 16, 16, 16, 16
   :header-rows: 0


2. Simulation Setup
===================

The Synthetic Eddy Method (SEM) boundary condition is applied at the inlet of the computational domain.
Solid fins are distributed across the floor to ensure the desired velocity and turbulence profiles during flow development length.
A Neumann boundary condition is applied at the remaining boundaries.

The building is positioned :math:`118H` from inlet, and 6 grid refinement levels (:math:`lvl\,0` to :math:`lvl\,5`) were adopted:

.. Top and lateral views, indicating the box and body refinements
.. figure_expand:: /_static/neighbour/grid.svg
   :alt: Computational Grid
   :figwidth: 100%
   :align: center

A 1:2 refinement ratio is estabilished between levels, and the simulation parameters at grid :math:`lvl\,5` were:

.. constant simulation parameters
.. csv-table:: Dimensionless Parameters
   :file: /_static/neighbour/c_01/params.csv
   :widths: 80, 20
   :header-rows: 0

The equivalent parameters in full scale are:

.. full scale parameters
.. csv-table:: Full-scale Parameters
   :file: /_static/neighbour/c_01/full_scale.csv
   :widths: 80, 20
   :header-rows: 0

The computational resources required were:

.. hardware and execution aspects
.. csv-table:: Computational Resources
   :file: /_static/neighbour/c_01/perf.csv
   :widths: 25, 15, 15, 15, 15, 15
   :header-rows: 0

3. Inflow
=========

An empty domain simulation is performed to measure the incident velocity and turbulence profiles.
A probe line is placed at the position where the building will be located.
The average velocities used for calculating the pressure coefficient and convective time scale are taken from this simulation.

Wind Profiles
-------------

.. profiles of velocity, turbulence and integral lenght scale
.. figure_expand:: /_static/neighbour/inflow/inflow_profile.svg
      :alt: Inflow Profile
      :max-width: 640px
      :align: center


Wind Spectra
------------
The power spectral density of the velocity components at height :math:`H` are compared with theoretical Von Kármán curves to validate the atmospheric flow.

.. spectra of velocity components
.. figure_expand:: /_static/neighbour/inflow/spectrum.svg
      :alt: Inflow Spectrum
      :figwidth: 100%
      :align: center

.. change spectrum legend to top left, over bottom left


4. Results: Local Statistics
============================

The pressure coefficient is calculated using the velocity at the building height :math:`H` and the reference pressure measured from a position far above the building. 
The same statistical processing of the pressure coefficient :math:`C_{p}` at each probe position is performed for both experimental and numerical data:

  - A sample of size (:math:`T / CTS`) is evaluated over moving averages of the original signals, with window size of 3s.
  - The processed data is subdivided in 10 intervals, from which the minimum and maximum values will be taken for each.
  - Those min/max values are fitted to a Gumbel distribution.
  - The shape parameters from Gubel distribution are then rescaled to 3600s.


Scatter on Points Statistics
----------------------------

The deviation between numerical and experimental data is quantified using the mean absolute error (MAE) and the normalized mean absolute error (NMAE):

.. math:: 
  \mathrm{MAE} = \frac{1}{N_{\mathrm{probes}}}\sum_{i=1}^{N_{\mathrm{probes}}}|q^{\left(i\right)}_{\mathrm{EXP}}-q^{\left(i\right)}_{\mathrm{NUM}}|

.. math::
  \mathrm{NMAE} = \frac{1}{N_{\mathrm{probes}}}\sum_{i=1}^{N_{\mathrm{probes}}}\frac{|q^{\left(i\right)}_{\mathrm{EXP}}-q^{\left(i\right)}_{\mathrm{NUM}}|}{\left[q^{\left(\mathrm{max}\right)}_{\mathrm{EXP}}-q^{\left(\mathrm{min}\right)}_{\mathrm{EXP}}\right]}\times 100

.. figure_expand:: /_static/neighbour/c_01/scatter_000.svg
  :alt: Scatter 000
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/scatter_023.svg
  :alt: Scatter 023
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/scatter_045.svg
  :alt: Scatter 045
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/scatter_068.svg
  :alt: Scatter 068
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/scatter_090.svg
  :alt: Scatter 090
  :figwidth: 100%
  :align: center
  

Mean and Peak Pressures
-----------------------

.. figure_expand:: /_static/neighbour/c_01/mean_peak_000.svg
  :alt: Mean and Peaks 000
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/mean_peak_023.svg
  :alt: Mean and Peaks 023
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/mean_peak_045.svg
  :alt: Mean and Peaks 045
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/mean_peak_068.svg
  :alt: Mean and Peaks 068
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/mean_peak_090.svg
  :alt: Mean and Peaks 090
  :max-width: 640px
  :align: center


RMS Pressures
-------------

.. figure_expand:: /_static/neighbour/c_01/rms_000.svg
  :alt: RMS 000
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/rms_023.svg
  :alt: RMS 023
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/rms_045.svg
  :alt: RMS 045
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/rms_068.svg
  :alt: RMS 068
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/rms_090.svg
  :alt: RMS 090
  :max-width: 640px
  :align: center


Skewness and Kurtosis
---------------------

.. figure_expand:: /_static/neighbour/c_01/highstats_000.svg
  :alt: Skew and Kurt 000
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/highstats_023.svg
  :alt: Skew and Kurt 023
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/highstats_045.svg
  :alt: Skew and Kurt 045
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/highstats_068.svg
  :alt: Skew and Kurt 068
  :max-width: 640px
  :align: center

.. figure_expand:: /_static/neighbour/c_01/highstats_090.svg
  :alt: Skew and Kurt 090
  :max-width: 640px
  :align: center


Pressure Spectrum
-----------------

.. figure_expand:: /_static/neighbour/c_01/spectra_000.svg
  :alt: Cp Spectrum 000
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/spectra_023.svg
  :alt: Cp Spectrum 023
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/spectra_045.svg
  :alt: Cp Spectrum 045
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/spectra_068.svg
  :alt: Cp Spectrum 068
  :figwidth: 100%
  :align: center

.. figure_expand:: /_static/neighbour/c_01/spectra_090.svg
  :alt: Cp Spectrum 090
  :figwidth: 100%
  :align: center

Execution Notes
===============

.. csv-table:: Execution Notes
   :file: /_static/neighbour/c_01/exec.csv
   :widths: 50, 50
   :header-rows: 0

Changelog
=========

* **30 Oct 2024**: Added scattering plots