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<div id="content" class="content">
<h1 class="title">Lattice Boltzmann simulation
<br />
<span class="subtitle">Jishnu Rajendran</span>
</h1>
<div class="abstract" id="orgb64ebb3">
<p>
Lattice Boltzmann methods are a family of computational methods for simulating the evolution of fluid flows in systems.
In this notebook, we implement a 2D square domain with rigid barrier using Lattice Boltzmann method.
The simulation is based on the LBM model and the boundary conditions are discussed in the following sections.
Instead of solving the <span class="underline">Navier–Stokes</span> equations directly, a fluid density on a lattice is simulated with streaming and collision (relaxation) processes. As a versatile model, the dynamics of the fluid can be simulated fairly straight. The LBM model can be made to mimic common fluid behaviour like vapour/liquid coexistence, and so fluid systems such as liquid droplets can be simulated.
</p>
</div>
<div id="outline-container-org73c475b" class="outline-2">
<h2 id="org73c475b"><span class="section-number-2">1.</span> Lattice Boltzmann simulation of a 2D square domain with rigid barrier</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-python"><span style="color: #83898d;">"""</span>
<span style="color: #83898d;">Lattice-Boltzmann method for fluid simulation</span>
<span style="color: #83898d;">Simple rectangular barrier</span>
<span style="color: #83898d;">@author: Jishnu</span>
<span style="color: #83898d;">"""</span>
<span style="color: #51afef;">import</span> numpy, time, matplotlib.pyplot, matplotlib.animation
<span style="color: #dcaeea;">height</span> = <span style="color: #da8548; font-weight: bold;">80</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">dimensions of lattice</span>
<span style="color: #dcaeea;">width</span> = <span style="color: #da8548; font-weight: bold;">200</span>
<span style="color: #dcaeea;">viscosity</span> = <span style="color: #da8548; font-weight: bold;">0.02</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">viscosity</span>
<span style="color: #dcaeea;">omega</span> = <span style="color: #da8548; font-weight: bold;">1</span> / (<span style="color: #da8548; font-weight: bold;">3</span>*viscosity + <span style="color: #da8548; font-weight: bold;">0.5</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">parameter for relaxation</span>
<span style="color: #dcaeea;">u0</span> = <span style="color: #da8548; font-weight: bold;">0.1</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">initial and in-flow speed</span>
<span style="color: #dcaeea;">f_n</span> = <span style="color: #da8548; font-weight: bold;">4.0</span>/<span style="color: #da8548; font-weight: bold;">9.0</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">lattice-Boltzmann weight factors</span>
<span style="color: #dcaeea;">o_n</span> = <span style="color: #da8548; font-weight: bold;">1.0</span>/<span style="color: #da8548; font-weight: bold;">9.0</span>
<span style="color: #dcaeea;">o_36</span> = <span style="color: #da8548; font-weight: bold;">1.0</span>/<span style="color: #da8548; font-weight: bold;">36.0</span>
<span style="color: #dcaeea;">performanceData</span> = <span style="color: #a9a1e1;">True</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">True if performance data is needed</span>
</pre>
</div>
<p>
Here we initialize the dimensions of the domain and the initial conditions of fluid flow. We will choose steady flow and initialise the density and velocity arrays.
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #5B6268;"># </span><span style="color: #5B6268;">Initialize arrays --steady rightward flow:</span>
<span style="color: #dcaeea;">n0</span> = f_n * (numpy.ones((height,width)) - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">particle densities along 9 directions</span>
<span style="color: #dcaeea;">nN</span> = o_n * (numpy.ones((height,width)) - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nS</span> = o_n * (numpy.ones((height,width)) - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nE</span> = o_n * (numpy.ones((height,width)) + <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nW</span> = o_n * (numpy.ones((height,width)) - <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nNE</span> = o_36 * (numpy.ones((height,width)) + <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nSE</span> = o_36 * (numpy.ones((height,width)) + <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nNW</span> = o_36 * (numpy.ones((height,width)) - <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nSW</span> = o_36 * (numpy.ones((height,width)) - <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">rho</span> = n0 + nN + nS + nE + nW + nNE + nSE + nNW + nSW <span style="color: #5B6268;"># </span><span style="color: #5B6268;">macroscopic density</span>
<span style="color: #dcaeea;">ux</span> = (nE + nNE + nSE - nW - nNW - nSW) / rho <span style="color: #5B6268;"># </span><span style="color: #5B6268;">macroscopic x velocity</span>
<span style="color: #dcaeea;">uy</span> = (nN + nNE + nNW - nS - nSE - nSW) / rho <span style="color: #5B6268;"># </span><span style="color: #5B6268;">macroscopic y velocity</span>
</pre>
</div>
</div>
<div id="outline-container-org4de0599" class="outline-3">
<h3 id="org4de0599"><span class="section-number-3">1.1.</span> Effects of a Barrier in a steady flow</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We choose a simple rectangle barrier in the domain.
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #dcaeea;">barrier</span> = numpy.zeros((height,width), <span style="color: #c678dd;">bool</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">True wherever there's a barrier</span>
<span style="color: #dcaeea;">barrier</span>[(height//<span style="color: #da8548; font-weight: bold;">2</span>)-<span style="color: #da8548; font-weight: bold;">8</span>:(height//<span style="color: #da8548; font-weight: bold;">2</span>)+<span style="color: #da8548; font-weight: bold;">8</span>, (height//<span style="color: #da8548; font-weight: bold;">2</span>)-<span style="color: #da8548; font-weight: bold;">4</span>:(height//<span style="color: #da8548; font-weight: bold;">2</span>)+<span style="color: #da8548; font-weight: bold;">4</span>] = <span style="color: #a9a1e1;">True</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">simple linear barrier</span>
<span style="color: #dcaeea;">barrierN</span> = numpy.roll(barrier, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">sites just north of barriers</span>
<span style="color: #dcaeea;">barrierS</span> = numpy.roll(barrier, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">sites just south of barriers</span>
<span style="color: #dcaeea;">barrierE</span> = numpy.roll(barrier, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">barrierW</span> = numpy.roll(barrier, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">barrierNE</span> = numpy.roll(barrierN, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">barrierNW</span> = numpy.roll(barrierN, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">barrierSE</span> = numpy.roll(barrierS, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">barrierSW</span> = numpy.roll(barrierS, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgb2682a2" class="outline-2">
<h2 id="orgb2682a2"><span class="section-number-2">2.</span> Move all particles by one step along their directions of motion (pbc):</h2>
<div class="outline-text-2" id="text-2">
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<pre class="src src-python"> <span style="color: #51afef;">def</span> <span style="color: #c678dd;">stream</span>():
<span style="color: #51afef;">global</span> nN, nS, nE, nW, nNE, nNW, nSE, nSW
<span style="color: #dcaeea;">nN</span> = numpy.roll(nN, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">axis 0 is north-south; + direction is north</span>
<span style="color: #dcaeea;">nNE</span> = numpy.roll(nNE, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>)
<span style="color: #dcaeea;">nNW</span> = numpy.roll(nNW, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>)
<span style="color: #dcaeea;">nS</span> = numpy.roll(nS, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>)
<span style="color: #dcaeea;">nSE</span> = numpy.roll(nSE, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>)
<span style="color: #dcaeea;">nSW</span> = numpy.roll(nSW, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">0</span>)
<span style="color: #dcaeea;">nE</span> = numpy.roll(nE, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">axis 1 is east-west; + direction is east</span>
<span style="color: #dcaeea;">nNE</span> = numpy.roll(nNE, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">nSE</span> = numpy.roll(nSE, <span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">nW</span> = numpy.roll(nW, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">nNW</span> = numpy.roll(nNW, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #dcaeea;">nSW</span> = numpy.roll(nSW, -<span style="color: #da8548; font-weight: bold;">1</span>, axis=<span style="color: #da8548; font-weight: bold;">1</span>)
<span style="color: #5B6268;"># </span><span style="color: #5B6268;">Using boolean arrays to handle barrier collisions (bounce-back):</span>
<span style="color: #dcaeea;">nN</span>[barrierN] = nS[barrier]
<span style="color: #dcaeea;">nS</span>[barrierS] = nN[barrier]
<span style="color: #dcaeea;">nE</span>[barrierE] = nW[barrier]
<span style="color: #dcaeea;">nW</span>[barrierW] = nE[barrier]
<span style="color: #dcaeea;">nNE</span>[barrierNE] = nSW[barrier]
<span style="color: #dcaeea;">nNW</span>[barrierNW] = nSE[barrier]
<span style="color: #dcaeea;">nSE</span>[barrierSE] = nNW[barrier]
<span style="color: #dcaeea;">nSW</span>[barrierSW] = nNE[barrier]
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<pre class="src src-python"><span style="color: #51afef;">def</span> <span style="color: #c678dd;">collide</span>():
<span style="color: #83898d;">"""</span>
<span style="color: #83898d;"> Calculates the collision step of the Lattice Boltzmann Method (LBM) algorithm.</span>
<span style="color: #83898d;"> Updates the macroscopic variables `rho`, `ux`, and `uy` based on the population</span>
<span style="color: #83898d;"> distributions `n0`, `nN`, `nS`, `nE`, `nW`, `nNE`, `nNW`, `nSE`, and `nSW`.</span>
<span style="color: #83898d;"> Parameters:</span>
<span style="color: #83898d;"> None</span>
<span style="color: #83898d;"> Returns:</span>
<span style="color: #83898d;"> None</span>
<span style="color: #83898d;"> """</span>
<span style="color: #51afef;">global</span> rho, ux, uy, n0, nN, nS, nE, nW, nNE, nNW, nSE, nSW
<span style="color: #dcaeea;">rho</span> = n0 + nN + nS + nE + nW + nNE + nSE + nNW + nSW
<span style="color: #dcaeea;">ux</span> = (nE + nNE + nSE - nW - nNW - nSW) / rho
<span style="color: #dcaeea;">uy</span> = (nN + nNE + nNW - nS - nSE - nSW) / rho
<span style="color: #dcaeea;">ux2</span> = ux * ux
<span style="color: #dcaeea;">uy2</span> = uy * uy
<span style="color: #dcaeea;">u2</span> = ux2 + uy2
<span style="color: #dcaeea;">omu215</span> = <span style="color: #da8548; font-weight: bold;">1</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u2
<span style="color: #dcaeea;">uxuy</span> = ux * uy
<span style="color: #dcaeea;">n0</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*n0 + omega * f_n * rho * omu215
<span style="color: #dcaeea;">nN</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nN + omega * o_n * rho * (omu215 + <span style="color: #da8548; font-weight: bold;">3</span>*uy + <span style="color: #da8548; font-weight: bold;">4.5</span>*uy2)
<span style="color: #dcaeea;">nS</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nS + omega * o_n * rho * (omu215 - <span style="color: #da8548; font-weight: bold;">3</span>*uy + <span style="color: #da8548; font-weight: bold;">4.5</span>*uy2)
<span style="color: #dcaeea;">nE</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nE + omega * o_n * rho * (omu215 + <span style="color: #da8548; font-weight: bold;">3</span>*ux + <span style="color: #da8548; font-weight: bold;">4.5</span>*ux2)
<span style="color: #dcaeea;">nW</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nW + omega * o_n * rho * (omu215 - <span style="color: #da8548; font-weight: bold;">3</span>*ux + <span style="color: #da8548; font-weight: bold;">4.5</span>*ux2)
<span style="color: #dcaeea;">nNE</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nNE + omega * o_36 * rho * (omu215 + <span style="color: #da8548; font-weight: bold;">3</span>*(ux+uy) + <span style="color: #da8548; font-weight: bold;">4.5</span>*(u2+<span style="color: #da8548; font-weight: bold;">2</span>*uxuy))
<span style="color: #dcaeea;">nNW</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nNW + omega * o_36 * rho * (omu215 + <span style="color: #da8548; font-weight: bold;">3</span>*(-ux+uy) + <span style="color: #da8548; font-weight: bold;">4.5</span>*(u2-<span style="color: #da8548; font-weight: bold;">2</span>*uxuy))
<span style="color: #dcaeea;">nSE</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nSE + omega * o_36 * rho * (omu215 + <span style="color: #da8548; font-weight: bold;">3</span>*(ux-uy) + <span style="color: #da8548; font-weight: bold;">4.5</span>*(u2-<span style="color: #da8548; font-weight: bold;">2</span>*uxuy))
<span style="color: #dcaeea;">nSW</span> = (<span style="color: #da8548; font-weight: bold;">1</span>-omega)*nSW + omega * o_36 * rho * (omu215 + <span style="color: #da8548; font-weight: bold;">3</span>*(-ux-uy) + <span style="color: #da8548; font-weight: bold;">4.5</span>*(u2+<span style="color: #da8548; font-weight: bold;">2</span>*uxuy))
<span style="color: #5B6268;"># </span><span style="color: #5B6268;">Force steady rightward flow at ends</span>
<span style="color: #5B6268;"># </span><span style="color: #5B6268;">no need to set 0, N, and S component</span>
<span style="color: #dcaeea;">nE</span>[:,<span style="color: #da8548; font-weight: bold;">0</span>] = o_n * (<span style="color: #da8548; font-weight: bold;">1</span> + <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nW</span>[:,<span style="color: #da8548; font-weight: bold;">0</span>] = o_n * (<span style="color: #da8548; font-weight: bold;">1</span> - <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nNE</span>[:,<span style="color: #da8548; font-weight: bold;">0</span>] = o_36 * (<span style="color: #da8548; font-weight: bold;">1</span> + <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nSE</span>[:,<span style="color: #da8548; font-weight: bold;">0</span>] = o_36 * (<span style="color: #da8548; font-weight: bold;">1</span> + <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nNW</span>[:,<span style="color: #da8548; font-weight: bold;">0</span>] = o_36 * (<span style="color: #da8548; font-weight: bold;">1</span> - <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
<span style="color: #dcaeea;">nSW</span>[:,<span style="color: #da8548; font-weight: bold;">0</span>] = o_36 * (<span style="color: #da8548; font-weight: bold;">1</span> - <span style="color: #da8548; font-weight: bold;">3</span>*u0 + <span style="color: #da8548; font-weight: bold;">4.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span> - <span style="color: #da8548; font-weight: bold;">1.5</span>*u0**<span style="color: #da8548; font-weight: bold;">2</span>)
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<pre class="src src-python"><span style="color: #5B6268;"># </span><span style="color: #5B6268;">Compute curl of the velocity field:</span>
<span style="color: #51afef;">def</span> <span style="color: #c678dd;">curl</span>(ux, uy):
<span style="color: #83898d;">"""</span>
<span style="color: #83898d;"> Calculates the curl of a vector field.</span>
<span style="color: #83898d;"> Parameters:</span>
<span style="color: #83898d;"> ux (numpy.ndarray): The x-component of the vector field.</span>
<span style="color: #83898d;"> uy (numpy.ndarray): The y-component of the vector field.</span>
<span style="color: #83898d;"> Returns:</span>
<span style="color: #83898d;"> numpy.ndarray: The curl of the vector field.</span>
<span style="color: #83898d;"> """</span>
<span style="color: #51afef;">return</span> numpy.roll(uy,-<span style="color: #da8548; font-weight: bold;">1</span>,axis=<span style="color: #da8548; font-weight: bold;">1</span>) - numpy.roll(uy,<span style="color: #da8548; font-weight: bold;">1</span>,axis=<span style="color: #da8548; font-weight: bold;">1</span>) - numpy.roll(ux,-<span style="color: #da8548; font-weight: bold;">1</span>,axis=<span style="color: #da8548; font-weight: bold;">0</span>) + numpy.roll(ux,<span style="color: #da8548; font-weight: bold;">1</span>,axis=<span style="color: #da8548; font-weight: bold;">0</span>)
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<h2 id="org522b278"><span class="section-number-2">3.</span> Visualization of the simulation</h2>
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<pre class="src src-python"><span style="color: #5B6268;"># </span><span style="color: #5B6268;">for animation.</span>
<span style="color: #dcaeea;">theFig</span> = matplotlib.pyplot.figure(figsize=(<span style="color: #da8548; font-weight: bold;">8</span>,<span style="color: #da8548; font-weight: bold;">3</span>))
<span style="color: #dcaeea;">fluidImage</span> = matplotlib.pyplot.imshow(curl(ux, uy), origin=<span style="color: #98be65;">'lower'</span>, norm=matplotlib.pyplot.Normalize(-.<span style="color: #da8548; font-weight: bold;">1</span>,.<span style="color: #da8548; font-weight: bold;">1</span>),
cmap=matplotlib.pyplot.get_cmap(<span style="color: #98be65;">'jet'</span>), interpolation=<span style="color: #98be65;">'none'</span>)
<span style="color: #dcaeea;">bImageArray</span> = numpy.zeros((height, width, <span style="color: #da8548; font-weight: bold;">4</span>), numpy.uint8) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">an RGBA image</span>
<span style="color: #dcaeea;">bImageArray</span>[barrier,<span style="color: #da8548; font-weight: bold;">3</span>] = <span style="color: #da8548; font-weight: bold;">255</span> <span style="color: #5B6268;"># </span><span style="color: #5B6268;">set alpha=255 barrier sites only</span>
<span style="color: #dcaeea;">barrierImage</span> = matplotlib.pyplot.imshow(bImageArray, origin=<span style="color: #98be65;">'lower'</span>, interpolation=<span style="color: #98be65;">'none'</span>)
<span style="color: #5B6268;"># </span><span style="color: #5B6268;">Function called for each successive animation frame:</span>
<span style="color: #dcaeea;">startTime</span> = time.perf_counter()
<span style="color: #5B6268;">#</span><span style="color: #5B6268;">frameList = open('frameList.txt','w') # file containing list of images</span>
<span style="color: #51afef;">def</span> <span style="color: #c678dd;">nextFrame</span>(arg): <span style="color: #5B6268;"># </span><span style="color: #5B6268;">(arg is the frame number, which we don't need)</span>
<span style="color: #51afef;">global</span> startTime
<span style="color: #51afef;">if</span> performanceData <span style="color: #51afef;">and</span> (arg%<span style="color: #da8548; font-weight: bold;">100</span> == <span style="color: #da8548; font-weight: bold;">0</span>) <span style="color: #51afef;">and</span> (arg > <span style="color: #da8548; font-weight: bold;">0</span>):
<span style="color: #dcaeea;">endTime</span> = time.perf_counter()
<span style="color: #c678dd;">print</span>( <span style="color: #98be65;">"%1.1f"</span> % (<span style="color: #da8548; font-weight: bold;">100</span>/(endTime-startTime)), <span style="color: #98be65;">'frames per second'</span> )
<span style="color: #dcaeea;">startTime</span> = endTime
<span style="color: #5B6268;">#</span><span style="color: #5B6268;">frameName = "frame%04d.png" % arg</span>
<span style="color: #5B6268;">#</span><span style="color: #5B6268;">matplotlib.pyplot.savefig(frameName)</span>
<span style="color: #5B6268;">#</span><span style="color: #5B6268;">frameList.write(frameName + '\n')</span>
<span style="color: #51afef;">for</span> step <span style="color: #51afef;">in</span> <span style="color: #c678dd;">range</span>(<span style="color: #da8548; font-weight: bold;">15</span>): <span style="color: #5B6268;"># </span><span style="color: #5B6268;">adjust number of steps for smooth animation</span>
stream()
collide()
fluidImage.set_array(curl(ux, uy))
<span style="color: #51afef;">return</span> (fluidImage, barrierImage) <span style="color: #5B6268;"># </span><span style="color: #5B6268;">return the figure elements to redraw</span>
<span style="color: #dcaeea;">animate</span> = matplotlib.animation.FuncAnimation(theFig, nextFrame, interval=<span style="color: #da8548; font-weight: bold;">0.5</span>, blit=<span style="color: #a9a1e1;">True</span>)
matplotlib.pyplot.show()
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<div id="postamble" class="status">
<p class="author">Author: Jishnu</p>
<p class="date">Created: 2023-12-27 Wed 20:18</p>
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