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<p id="example-vonkarman-py">Von Karman street using finite differences</p>
<p><strong>Python source code:</strong> <a class="reference download internal" href="../_downloads/VonKarman.py"><tt class="xref download docutils literal"><span class="pre">VonKarman.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="k">if</span> <span class="s">'qt'</span> <span class="ow">in</span> <span class="n">plt</span><span class="o">.</span><span class="n">get_backend</span><span class="p">()</span><span class="o">.</span><span class="n">lower</span><span class="p">():</span>
<span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">PyQt4</span> <span class="kn">import</span> <span class="n">QtGui</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">PySide</span> <span class="kn">import</span> <span class="n">QtGui</span>
<span class="kn">import</span> <span class="nn">scipy.sparse</span> <span class="kn">as</span> <span class="nn">sp</span>
<span class="kn">from</span> <span class="nn">scipy.sparse</span> <span class="kn">import</span> <span class="n">spdiags</span>
<span class="kn">from</span> <span class="nn">scipy.sparse.linalg.dsolve</span> <span class="kn">import</span> <span class="n">spsolve</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">CFL</span><span class="p">():</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">u</span>
<span class="k">global</span> <span class="n">v</span>
<span class="n">umax</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">u</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span><span class="mf">0.01</span><span class="p">);</span>
<span class="n">vmax</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">v</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span><span class="mf">0.01</span><span class="p">);</span>
<span class="n">vcfl</span> <span class="o">=</span> <span class="mf">0.8</span><span class="o">*</span><span class="nb">min</span><span class="p">(</span><span class="n">dx</span><span class="o">/</span><span class="n">umax</span><span class="p">,</span><span class="n">dy</span><span class="o">/</span><span class="n">vmax</span><span class="p">);</span>
<span class="k">return</span> <span class="n">vcfl</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">Forme</span><span class="p">():</span>
<span class="c"># Donne la forme de l obstacle</span>
<span class="k">global</span> <span class="n">Fe</span>
<span class="k">global</span> <span class="n">tactuel</span>
<span class="k">global</span> <span class="n">M</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">L</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="c"># Initialisation de la matrice de forme</span>
<span class="n">Fe</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Centrage de la forme en ordonnee</span>
<span class="n">ctry</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span>
<span class="c"># Centrage de la forme en abscisse</span>
<span class="n">ctrx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">int</span><span class="p">(</span><span class="n">M</span><span class="o">/</span><span class="mi">5</span><span class="p">)</span>
<span class="c"># Forme 1: obstacle spherique immobile</span>
<span class="k">for</span> <span class="n">il</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">int</span><span class="p">(</span><span class="n">L</span><span class="o">/</span><span class="n">dy</span><span class="p">),</span><span class="n">np</span><span class="o">.</span><span class="n">int</span><span class="p">(</span><span class="n">L</span><span class="o">/</span><span class="n">dy</span><span class="p">)):</span> <span class="c"># indice en ligne</span>
<span class="n">largeur</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">L</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="o">-</span><span class="p">(</span><span class="n">dy</span><span class="o">*</span><span class="n">il</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ic</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">int</span><span class="p">(</span><span class="n">largeur</span><span class="o">/</span><span class="n">dx</span><span class="p">)</span> <span class="c"># indice en colonne</span>
<span class="k">for</span> <span class="n">jl</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">ctrx</span><span class="o">-</span><span class="n">ic</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="n">ctrx</span><span class="o">+</span><span class="n">ic</span><span class="p">):</span>
<span class="n">Fe</span><span class="p">[</span><span class="n">ctry</span><span class="o">+</span><span class="n">il</span><span class="p">,</span><span class="n">jl</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">Advect</span><span class="p">():</span>
<span class="c"># Calcule la valeur interpolee qui correspond a l advection </span>
<span class="c"># a la vitesse au temps n </span>
<span class="k">global</span> <span class="n">u</span>
<span class="k">global</span> <span class="n">v</span>
<span class="k">global</span> <span class="n">color</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">dt</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">M</span>
<span class="k">global</span> <span class="n">Resu</span>
<span class="k">global</span> <span class="n">Resv</span>
<span class="c"># Matrice avec des 1 quand on va a droite, 0 a gauche ou au centre</span>
<span class="n">Mx2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">)))</span>
<span class="n">Mx1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span><span class="o">-</span><span class="n">Mx2</span>
<span class="c"># Matrice avec des 1 quand on va en haut, 0 en bas ou au centre</span>
<span class="n">My2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">)))</span>
<span class="n">My1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span><span class="o">-</span><span class="n">My2</span>
<span class="c"># Matrices en valeurs absolues pour u et v</span>
<span class="n">au</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">av</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="c"># Matrices des coefficients respectivement central, exterieur, meme x, meme y</span>
<span class="n">Cc</span> <span class="o">=</span> <span class="p">(</span><span class="n">dx</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span><span class="o">-</span><span class="n">au</span><span class="o">*</span><span class="n">dt</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">dy</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span><span class="o">-</span><span class="n">av</span><span class="o">*</span><span class="n">dt</span><span class="p">)</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="n">dy</span>
<span class="n">Ce</span> <span class="o">=</span> <span class="n">dt</span><span class="o">*</span><span class="n">dt</span><span class="o">*</span><span class="n">au</span><span class="o">*</span><span class="n">av</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="n">dy</span>
<span class="n">Cmx</span> <span class="o">=</span> <span class="p">(</span><span class="n">dx</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span><span class="o">-</span><span class="n">dt</span><span class="o">*</span><span class="n">au</span><span class="p">)</span><span class="o">*</span><span class="n">av</span><span class="o">*</span><span class="n">dt</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="n">dy</span>
<span class="n">Cmy</span> <span class="o">=</span> <span class="n">dt</span><span class="o">*</span><span class="n">au</span><span class="o">*</span><span class="p">(</span><span class="n">dy</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="n">M</span><span class="o">-</span><span class="mi">2</span><span class="p">))</span><span class="o">-</span><span class="n">dt</span><span class="o">*</span><span class="n">av</span><span class="p">)</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="n">dy</span>
<span class="c"># Calcul des matrices de resultat pour les vitesses u et v</span>
<span class="n">Resu</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="n">Cc</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span> \
<span class="n">Ce</span><span class="o">*</span><span class="p">(</span><span class="n">Mx1</span><span class="o">*</span><span class="n">My1</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx1</span><span class="o">*</span><span class="n">My2</span><span class="o">*</span><span class="n">u</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">My1</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">2</span><span class="p">:,:</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">My2</span><span class="o">*</span><span class="n">u</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">+</span> \
<span class="n">Cmx</span><span class="o">*</span><span class="p">(</span><span class="n">My1</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">My2</span><span class="o">*</span><span class="n">u</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">+</span> \
<span class="n">Cmy</span><span class="o">*</span><span class="p">(</span><span class="n">Mx1</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
<span class="n">Resv</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="n">Cc</span><span class="o">*</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span> \
<span class="n">Ce</span><span class="o">*</span><span class="p">(</span><span class="n">Mx1</span><span class="o">*</span><span class="n">My1</span><span class="o">*</span><span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx1</span><span class="o">*</span><span class="n">My2</span><span class="o">*</span><span class="n">v</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">My1</span><span class="o">*</span><span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">:,:</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">My2</span><span class="o">*</span><span class="n">v</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">+</span> \
<span class="n">Cmx</span><span class="o">*</span><span class="p">(</span><span class="n">My1</span><span class="o">*</span><span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">My2</span><span class="o">*</span><span class="n">v</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">+</span> \
<span class="n">Cmy</span><span class="o">*</span><span class="p">(</span><span class="n">Mx1</span><span class="o">*</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
<span class="n">color</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="n">Cc</span><span class="o">*</span><span class="n">color</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span> \
<span class="n">Ce</span><span class="o">*</span><span class="p">(</span><span class="n">Mx1</span><span class="o">*</span><span class="n">My1</span><span class="o">*</span><span class="n">color</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx1</span><span class="o">*</span><span class="n">My2</span><span class="o">*</span><span class="n">color</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">My1</span><span class="o">*</span><span class="n">color</span><span class="p">[</span><span class="mi">2</span><span class="p">:,:</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">My2</span><span class="o">*</span><span class="n">color</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">+</span> \
<span class="n">Cmx</span><span class="o">*</span><span class="p">(</span><span class="n">My1</span><span class="o">*</span><span class="n">color</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">My2</span><span class="o">*</span><span class="n">color</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">+</span> \
<span class="n">Cmy</span><span class="o">*</span><span class="p">(</span><span class="n">Mx1</span><span class="o">*</span><span class="n">color</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">+</span><span class="n">Mx2</span><span class="o">*</span><span class="n">color</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">Laplacien_u</span><span class="p">():</span>
<span class="c"># Calcule le laplacien scalaire rst(i,j) du champ scalaire u(i,j)</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">M</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">u</span>
<span class="n">rst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">coefx</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="n">dx</span>
<span class="n">coefy</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">dy</span><span class="o">/</span><span class="n">dy</span>
<span class="n">coef0</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">coefx</span> <span class="o">+</span> <span class="n">coefy</span><span class="p">)</span>
<span class="n">rst</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span> <span class="o">+</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">coefx</span> \
<span class="o">+</span> <span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">u</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">*</span><span class="n">coefy</span> \
<span class="o">-</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">coef0</span>
<span class="k">return</span> <span class="n">rst</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">Laplacien_v</span><span class="p">():</span>
<span class="c"># Calcule le laplacien scalaire rst(i,j) du champ scalaire v(i,j)</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">M</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">v</span>
<span class="n">rst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">coefx</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="n">dx</span>
<span class="n">coefy</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">dy</span><span class="o">/</span><span class="n">dy</span>
<span class="n">coef0</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">coefx</span> <span class="o">+</span> <span class="n">coefy</span><span class="p">)</span>
<span class="n">rst</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span> <span class="o">+</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">*</span><span class="n">coefx</span> \
<span class="o">+</span> <span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">v</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">*</span><span class="n">coefy</span> \
<span class="o">-</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">coef0</span>
<span class="k">return</span> <span class="n">rst</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">BuildLpl</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">):</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">LAP2</span>
<span class="c"># Definition of the 1D Lalace operator</span>
<span class="n">dataN</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="p">),</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="p">),</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">N</span><span class="p">)]</span> <span class="c"># Diagonal terms</span>
<span class="n">dataN</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="mi">2</span> <span class="c"># SF low</span>
<span class="n">dataN</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">N</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span><span class="o">=</span><span class="mi">2</span> <span class="c"># SF top</span>
<span class="n">dataM</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">M</span><span class="p">),</span><span class="o">-</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">M</span><span class="p">),</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">M</span><span class="p">)]</span> <span class="c"># Diagonal terms</span>
<span class="n">dataM</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="mi">2</span> <span class="c"># SF left</span>
<span class="n">offsets</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span> <span class="c"># Their positions</span>
<span class="n">DXX</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">dia_matrix</span><span class="p">(</span> <span class="p">(</span><span class="n">dataM</span><span class="p">,</span><span class="n">offsets</span><span class="p">),</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">M</span><span class="p">,</span><span class="n">M</span><span class="p">))</span><span class="o">/</span><span class="n">dx</span><span class="o">**</span><span class="mi">2</span>
<span class="n">DYY</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">dia_matrix</span><span class="p">(</span> <span class="p">(</span><span class="n">dataN</span><span class="p">,</span><span class="n">offsets</span><span class="p">),</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="n">N</span><span class="p">))</span><span class="o">/</span><span class="n">dy</span><span class="o">**</span><span class="mi">2</span>
<span class="c"># 2D Laplace operator</span>
<span class="n">LAP2</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">kron</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="n">N</span><span class="p">),</span><span class="n">DXX</span><span class="p">)</span><span class="o">+</span><span class="n">sp</span><span class="o">.</span><span class="n">kron</span><span class="p">(</span><span class="n">DYY</span><span class="p">,</span><span class="n">sp</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">M</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">ResoLpl</span><span class="p">(</span><span class="n">f22D</span><span class="p">,</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">):</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">LAP2</span>
<span class="n">f2</span> <span class="o">=</span> <span class="n">f22D</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N</span><span class="o">*</span><span class="n">M</span><span class="p">)</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">spsolve</span><span class="p">(</span><span class="n">LAP2</span><span class="p">,</span><span class="n">f2</span><span class="p">)</span> <span class="c"># Solving the linear system</span>
<span class="n">u2D</span><span class="o">=</span><span class="n">T</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">)</span>
<span class="k">return</span> <span class="n">u2D</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">div</span><span class="p">():</span>
<span class="c"># Calcule la divergence de (ustar,vstar) et la renvoie dans divstar</span>
<span class="k">global</span> <span class="n">ustar</span>
<span class="k">global</span> <span class="n">vstar</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">divstar</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">M</span>
<span class="n">divstar</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">ustar</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:</span><span class="n">M</span><span class="p">]</span><span class="o">-</span><span class="n">ustar</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="p">(</span><span class="n">vstar</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">vstar</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">/</span><span class="n">dy</span><span class="o">/</span><span class="mi">2</span>
<span class="c">####</span>
<span class="k">def</span> <span class="nf">grad</span><span class="p">():</span>
<span class="c"># Calcule le gradient de phi</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">phi</span>
<span class="k">global</span> <span class="n">gradphix</span>
<span class="k">global</span> <span class="n">gradphiy</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">M</span>
<span class="n">gradphix</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">phi</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">:]</span><span class="o">-</span><span class="n">phi</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,:</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span><span class="o">/</span><span class="n">dx</span><span class="o">/</span><span class="mi">2</span>
<span class="n">gradphiy</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">phi</span><span class="p">[</span><span class="mi">2</span><span class="p">:,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">phi</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="o">/</span><span class="n">dy</span><span class="o">/</span><span class="mi">2</span>
<span class="c">#### Programme principal</span>
<span class="c"># Variables globales</span>
<span class="k">global</span> <span class="n">L</span>
<span class="k">global</span> <span class="n">M</span>
<span class="k">global</span> <span class="n">N</span>
<span class="k">global</span> <span class="n">dx</span>
<span class="k">global</span> <span class="n">dy</span>
<span class="k">global</span> <span class="n">dt</span>
<span class="k">global</span> <span class="n">u</span>
<span class="k">global</span> <span class="n">v</span>
<span class="k">global</span> <span class="n">color</span>
<span class="k">global</span> <span class="n">Fe</span>
<span class="k">global</span> <span class="n">tactuel</span>
<span class="k">global</span> <span class="n">Resu</span>
<span class="k">global</span> <span class="n">Resv</span>
<span class="k">global</span> <span class="n">ustar</span>
<span class="k">global</span> <span class="n">vstar</span>
<span class="k">global</span> <span class="n">divstar</span>
<span class="k">global</span> <span class="n">gradphix</span>
<span class="k">global</span> <span class="n">gradphiy</span>
<span class="k">global</span> <span class="n">phi</span>
<span class="k">global</span> <span class="n">LAP2</span>
<span class="c"># Valeur des parametres d adimentionnement</span>
<span class="n">L</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">U</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">Nu</span> <span class="o">=</span> <span class="mf">1.e-6</span>
<span class="n">Re</span> <span class="o">=</span> <span class="n">U</span><span class="o">*</span><span class="n">L</span><span class="o">/</span><span class="n">Nu</span>
<span class="c"># Taille adimensionnee du domaine</span>
<span class="c"># Longueur</span>
<span class="n">Long</span> <span class="o">=</span> <span class="mi">20</span><span class="o">*</span><span class="n">L</span>
<span class="c"># Largeur</span>
<span class="n">Larg</span> <span class="o">=</span> <span class="mi">10</span><span class="o">*</span><span class="n">L</span>
<span class="c"># Nombre de points (entoure de points fantomes)</span>
<span class="c"># Nombre de points sur l axe (Ox) pair</span>
<span class="n">M</span> <span class="o">=</span> <span class="mi">201</span>
<span class="c"># Nombre de points sur l axe (Oy) impair</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>
<span class="c"># Valeurs des elements differentiels</span>
<span class="n">dx</span> <span class="o">=</span> <span class="p">(</span><span class="mf">20.</span><span class="o">*</span><span class="n">L</span><span class="p">)</span><span class="o">/</span><span class="n">M</span>
<span class="n">dy</span> <span class="o">=</span> <span class="p">(</span><span class="mf">10.</span><span class="o">*</span><span class="n">L</span><span class="p">)</span><span class="o">/</span><span class="n">N</span>
<span class="c"># Maillage pour affichage</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">Long</span><span class="p">,</span><span class="n">M</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">Larg</span><span class="p">,</span><span class="n">N</span><span class="p">)</span>
<span class="p">[</span><span class="n">xx</span><span class="p">,</span><span class="n">yy</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span>
<span class="c"># Parametres temporels</span>
<span class="n">tini</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">tfin</span> <span class="o">=</span> <span class="mi">10</span>
<span class="n">tactuel</span> <span class="o">=</span> <span class="mi">0</span>
<span class="c"># ATTENTION: calculer la CFL a chaque iteration...</span>
<span class="n">dt</span> <span class="o">=</span> <span class="mf">0.01</span>
<span class="c"># Valeurs des vitesses</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Matrices dans lesquelles se trouvent les extrapolations</span>
<span class="n">Resu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">Resv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Definition des matrices ustar vstar</span>
<span class="n">ustar</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">vstar</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Definition des matrices color</span>
<span class="n">color</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Definition de divstar</span>
<span class="n">divstar</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Definition de phi</span>
<span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">gradphix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="n">gradphiy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">))</span>
<span class="c"># Construction de la matrice de Laplace</span>
<span class="n">BuildLpl</span><span class="p">(</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">)</span>
<span class="c"># Parametrisation des plots</span>
<span class="n">niter</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">nitermax</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="c"># Forme de l obstacle donnee par une matrice</span>
<span class="n">Forme</span><span class="p">()</span>
<span class="c"># Mode interactif</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ion</span><span class="p">()</span>
<span class="c"># ITERATIONS</span>
<span class="k">for</span> <span class="n">niter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">nitermax</span><span class="p">):</span>
<span class="n">dt</span> <span class="o">=</span> <span class="n">CFL</span><span class="p">()</span>
<span class="c"># Colorant</span>
<span class="n">color</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">+</span><span class="mi">10</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span><span class="o">=</span><span class="mf">1.0</span>
<span class="n">color</span><span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">N</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span><span class="o">=</span><span class="mf">1.0</span>
<span class="c"># Etape d'advection semie-Lagrangienne</span>
<span class="n">Advect</span><span class="p">()</span>
<span class="c"># Premiere etape d iteration</span>
<span class="n">ustar</span> <span class="o">=</span> <span class="n">dt</span><span class="o">/</span><span class="n">Re</span><span class="o">*</span><span class="n">Laplacien_u</span><span class="p">()</span><span class="o">+</span><span class="n">Resu</span>
<span class="n">vstar</span> <span class="o">=</span> <span class="n">dt</span><span class="o">/</span><span class="n">Re</span><span class="o">*</span><span class="n">Laplacien_v</span><span class="p">()</span><span class="o">+</span><span class="n">Resv</span>
<span class="c"># Conditions aux limites</span>
<span class="c"># entree</span>
<span class="n">ustar</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mf">1.0</span> <span class="c">#np.ones(N)</span>
<span class="n">vstar</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mf">0.0</span> <span class="c">#np.zeros(N)</span>
<span class="c"># haut</span>
<span class="n">ustar</span><span class="p">[</span><span class="n">N</span><span class="o">-</span><span class="mi">1</span><span class="p">,:]</span><span class="o">=</span><span class="n">ustar</span><span class="p">[</span><span class="n">N</span><span class="o">-</span><span class="mi">3</span><span class="p">,:]</span>
<span class="n">vstar</span><span class="p">[</span><span class="n">N</span><span class="o">-</span><span class="mi">1</span><span class="p">,:]</span><span class="o">=</span><span class="mf">0.0</span> <span class="c">#np.zeros(M)</span>
<span class="c"># bas</span>
<span class="n">ustar</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span><span class="o">=</span><span class="n">ustar</span><span class="p">[</span><span class="mi">2</span><span class="p">,:]</span>
<span class="n">vstar</span><span class="p">[</span><span class="mi">0</span><span class="p">,:]</span><span class="o">=</span><span class="mf">0.0</span> <span class="c">#np.zeros(M)</span>
<span class="c"># sortie</span>
<span class="n">ustar</span><span class="p">[:,</span><span class="n">M</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="n">ustar</span><span class="p">[:,</span><span class="n">M</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span>
<span class="n">vstar</span><span class="p">[:,</span><span class="n">M</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="n">vstar</span><span class="p">[:,</span><span class="n">M</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span>
<span class="c"># Prise en compte de l obstacle</span>
<span class="n">ustar</span><span class="o">*=</span><span class="n">Fe</span>
<span class="n">vstar</span><span class="o">*=</span><span class="n">Fe</span>
<span class="c"># Deuxieme etape d iteration</span>
<span class="c"># Resolution de laplacien phi = div ustar</span>
<span class="n">div</span><span class="p">()</span>
<span class="n">phi</span> <span class="o">=</span> <span class="n">ResoLpl</span><span class="p">(</span><span class="n">divstar</span><span class="p">,</span><span class="n">N</span><span class="p">,</span><span class="n">M</span><span class="p">)</span>
<span class="c"># Troisieme etape</span>
<span class="n">grad</span><span class="p">()</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">ustar</span> <span class="o">-</span> <span class="n">gradphix</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">vstar</span> <span class="o">-</span> <span class="n">gradphiy</span>
<span class="k">if</span> <span class="p">(</span><span class="n">niter</span><span class="o">%</span><span class="mi">10</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
<span class="k">print</span> <span class="s">"iteration: </span><span class="si">%d</span><span class="s">"</span> <span class="o">%</span><span class="n">niter</span>
<span class="n">plotlabel</span> <span class="o">=</span> <span class="s">"t = </span><span class="si">%1.2f</span><span class="s">"</span> <span class="o">%</span><span class="p">(</span><span class="n">niter</span> <span class="o">*</span> <span class="n">dt</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">yy</span><span class="p">,</span><span class="n">color</span><span class="p">,</span><span class="n">shading</span><span class="o">=</span><span class="s">'flat'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">clim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">yy</span><span class="p">,</span><span class="n">Fe</span><span class="p">,</span><span class="n">hold</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span><span class="n">colors</span><span class="o">=</span><span class="s">'b'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">plotlabel</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">'image'</span><span class="p">)</span>
<span class="c"># plt.savefig('image%d.png' %(niter/10))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
<span class="k">if</span> <span class="s">'qt'</span> <span class="ow">in</span> <span class="n">plt</span><span class="o">.</span><span class="n">get_backend</span><span class="p">()</span><span class="o">.</span><span class="n">lower</span><span class="p">():</span>
<span class="n">QtGui</span><span class="o">.</span><span class="n">qApp</span><span class="o">.</span><span class="n">processEvents</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">u</span><span class="o">*=</span><span class="n">Fe</span>
<span class="n">v</span><span class="o">*=</span><span class="n">Fe</span>
<span class="n">plt</span><span class="o">.</span><span class="n">streamplot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">yy</span><span class="p">,</span><span class="n">u</span><span class="p">,</span><span class="n">v</span><span class="p">,</span><span class="n">color</span><span class="o">=</span><span class="s">'k'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">yy</span><span class="p">,</span><span class="n">Fe</span><span class="p">,</span><span class="n">hold</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span><span class="n">colors</span><span class="o">=</span><span class="s">'b'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">'image'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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