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‎.doctrees/6_inputdeck.doctree‎

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‎.doctrees/environment.pickle‎

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‎6_inputdeck.html‎

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<li class="toctree-l2"><a class="reference internal" href="#input-and-range-control">Input and Range Control</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#numerical-methods">Numerical Methods</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#dynamic-lcs-window">Dynamic LCS Window</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#utilizations">Utilizations</a></li>
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</ul>
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</li>
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<li class="toctree-l1"><a class="reference internal" href="7_command.html">Command-Line Mode (Commands)</a></li>
@@ -158,6 +159,11 @@ <h2>Input and Range Control<a class="headerlink" href="#input-and-range-control"
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<td><p><code class="docutils literal notranslate"><span class="pre">&lt;float&gt;</span></code></p></td>
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<td></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">physical_dt</span></code></p></td>
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<td><p>Physical time step between two input frames</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">&lt;float&gt;</span></code></p></td>
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<td></td>
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</tr>
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</tbody>
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</table>
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</section>
@@ -205,12 +211,12 @@ <h2>Numerical Methods<a class="headerlink" href="#numerical-methods" title="Link
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">advc_method</span></code></p></td>
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<td><p>Lagrangian advection scheme</p></td>
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<td><p>(<code class="docutils literal notranslate"><span class="pre">Euler</span></code>)</p></td>
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<td><p>Simple and fast Euler stepping with</p></td>
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<td><p>Simple and fast Euler stepping with <span class="math notranslate nohighlight">\(O(h^1)\)</span> error.</p></td>
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</tr>
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<tr class="row-odd"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">RK2</span></code></p></td>
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<td><p>Runge–Kutta 2 with <span class="math notranslate nohighlight">\(O(h^3)\)</span> error.</p></td>
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<td><p>Runge–Kutta 2 with <span class="math notranslate nohighlight">\(O(h^2)\)</span> error.</p></td>
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</tr>
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<tr class="row-even"><td></td>
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<td></td>
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<td><p>Runge–Kutta 6 with <span class="math notranslate nohighlight">\(O(h^6)\)</span> error.</p></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">interp_method</span></code></p></td>
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<td><p>Interpolation method</p></td>
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<td><p>Interpolation method for velocity fields</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">trilinear</span></code></p></td>
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<td><p>NA</p></td>
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<td><p>Simple and fast triliear interpolation method. Very fast on GPUs.</p></td>
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</tr>
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<tr class="row-odd"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">tricubic</span></code></p></td>
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<td><p>(<code class="docutils literal notranslate"><span class="pre">tricubic</span></code>)</p></td>
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<td></td>
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</tr>
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<tr class="row-even"><td></td>
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</tr>
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<tr class="row-odd"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">reflect</span></code></p></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">WENO</span></code></p></td>
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<td><p>Weighted Essentially Non-Oscillatory (WENO) scheme with shockwave capture capability.</p></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">grad_order</span></code></p></td>
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<td><p>The method (order) of gradient discretization</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">2</span></code></p></td>
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<td><p>(<code class="docutils literal notranslate"><span class="pre">2</span></code>)</p></td>
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<td><p>2nd-order central difference.</p></td>
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</tr>
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<tr class="row-odd"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">4</span></code></p></td>
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<td><p>4th-order central difference.</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> 4th-order central difference.</p></td>
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</tr>
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<tr class="row-even"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">6</span></code></p></td>
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<td><p>6th-order central difference.</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> 6th-order central difference.</p></td>
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</tr>
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<tr class="row-odd"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">100</span></code></p></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> Global Fast Fourier Transform (FFT) with finite order. Compute extremely intensive!</p></td>
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</tr>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">Eigen_method</span></code></p></td>
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<td><p>Eigenvalue computation method</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">&lt;string&gt;</span></code></p></td>
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<td><p>NA</p></td>
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<td><p>Solver for max eigenvalue of Cauchy–Green tensor</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">eigmax_sym3</span></code></p></td>
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<td><p>Closed-form cubic eigenvalue solver for symmetric 3×3 matrices (noniterative solver).</p></td>
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</tr>
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<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">if_visual</span></code></p></td>
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<td><p>Glace visualization enabler</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">0</span></code> or <code class="docutils literal notranslate"><span class="pre">1</span></code></p></td>
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<td><p>Take a pop-up glance on the results after computation for check with a rudimentary appearance.</p></td>
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<tr class="row-odd"><td></td>
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<td></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">jacobi</span></code></p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> Jacobi eigenvalue algorithm (iterative).</p></td>
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</tr>
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</tbody>
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</table>
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<p>As for your reference, and configured as defaults, the <em>Berkeley LCS Tutorials</em> used <code class="docutils literal notranslate"><span class="pre">RK4</span></code> for advection, interpolated by <code class="docutils literal notranslate"><span class="pre">tricubic</span></code>. Although non detailed, <code class="docutils literal notranslate"><span class="pre">grad_order=2</span></code> was employed by them from the equation, supposing the mesh is sufficiently refined.
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Please always notice that, although providing much better numerical precision and looks cool in papers, high-order methods could be resource-consuming, even hundreds of times.</p>
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</section>
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<section id="dynamic-lcs-window">
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<h2>Dynamic LCS Window<a class="headerlink" href="#dynamic-lcs-window" title="Link to this heading"></a></h2>
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</tr>
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</tbody>
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</table>
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</section>
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<section id="utilizations">
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<h2>Utilizations<a class="headerlink" href="#utilizations" title="Link to this heading"></a></h2>
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<table class="docutils align-default">
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<thead>
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<tr class="row-odd"><th class="head"><p>Key</p></th>
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<th class="head"><p>Description</p></th>
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<th class="head"><p>Value(s)</p></th>
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<th class="head"><p>Explaination</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">if_visual</span></code></p></td>
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<td><p>Glace visualization enabler</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">0</span></code> or <code class="docutils literal notranslate"><span class="pre">1</span></code></p></td>
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<td><p>Take a pop-up glance on the results after computation for check with a rudimentary appearance.</p></td>
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</tr>
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</tbody>
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</table>
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<p id="flow-vars">Flow So</p>
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</section>
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</section>

‎_sources/6_inputdeck.rst.txt‎

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@@ -33,6 +33,8 @@ Input and Range Control
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``dt`` | Time step for particle advection in frames | ``<float>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``physical_dt`` | Physical time step between two input frames | ``<float>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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Numerical Methods
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---------------------------------
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``periodic`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``advc_method`` | Lagrangian advection scheme | (``Euler``) | Simple and fast Euler stepping with |
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| ``advc_method`` | Lagrangian advection scheme | (``Euler``) | Simple and fast Euler stepping with :math:`O(h^1)` error. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``RK2`` | Runge–Kutta 2 with :math:`O(h^3)` error. |
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| | | ``RK2`` | Runge–Kutta 2 with :math:`O(h^2)` error. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``RK4`` | Runge–Kutta 4 with :math:`O(h^4)` error. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``RK6`` | Runge–Kutta 6 with :math:`O(h^6)` error. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``interp_method`` | Interpolation method | ``trilinear`` | NA |
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| ``interp_method`` | Interpolation method for velocity fields | ``trilinear`` | Simple and fast triliear interpolation method. Very fast on GPUs. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``tricubic`` | |
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| | | (``tricubic``) | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``hermite`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``reflect`` | |
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| | | ``WENO`` | Weighted Essentially Non-Oscillatory (WENO) scheme with shockwave capture capability. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``grad_order`` | The method (order) of gradient discretization | ``2`` | 2nd-order central difference. |
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| ``grad_order`` | The method (order) of gradient discretization | (``2``) | 2nd-order central difference. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``4`` | 4th-order central difference. |
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| | | ``4`` | ``I.P.`` 4th-order central difference. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``6`` | 6th-order central difference. |
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| | | ``6`` | ``I.P.`` 6th-order central difference. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | ``100`` | |
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| | | ``100`` | ``I.P.`` Global Fast Fourier Transform (FFT) with finite order. Compute extremely intensive! |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``Eigen_method`` | Eigenvalue computation method | ``<string>`` | NA |
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| ``Eigen_method`` | Solver for max eigenvalue of Cauchy–Green tensor | ``eigmax_sym3`` | Closed-form cubic eigenvalue solver for symmetric 3×3 matrices (noniterative solver). |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``if_visual`` | Glace visualization enabler | ``0`` or ``1`` | Take a pop-up glance on the results after computation for check with a rudimentary appearance. |
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| | | ``jacobi`` | ``I.P.`` Jacobi eigenvalue algorithm (iterative). |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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As for your reference, and configured as defaults, the *Berkeley LCS Tutorials* used ``RK4`` for advection, interpolated by ``tricubic``. Although non detailed, ``grad_order=2`` was employed by them from the equation, supposing the mesh is sufficiently refined.
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Please always notice that, although providing much better numerical precision and looks cool in papers, high-order methods could be resource-consuming, even hundreds of times.
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Dynamic LCS Window
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---------------------------------
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| ``win_step`` | Window step for dynamic LCS | ``<float>`` | Stepping in frames. Better smaller than ``win_size/2`` for capturing dynamic patterns. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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Utilizations
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-------------------
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| Key | Description | Value(s) | Explaination |
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+===================+======================================================+=========================+=========================================================================================================+
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| ``if_visual`` | Glace visualization enabler | ``0`` or ``1`` | Take a pop-up glance on the results after computation for check with a rudimentary appearance. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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.. _flow_vars:
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