deploy: 8fe0357

Author: hweifluids

.doctrees/3_numerical.doctree

@@ -45,8 +45,18 @@
               <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="1_requirements.html">Requirements and Quickstart</a></li>
 <li class="toctree-l1"><a class="reference internal" href="2_theory.html">Theory of FTLE and LCS</a></li>
-<li class="toctree-l1 current"><a class="current reference internal" href="#">Numerical Methods</a></li>
-<li class="toctree-l1"><a class="reference internal" href="#computational-density-and-comparison">Computational Density and Comparison</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Numerical Methods</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#wall-treatment">Wall Treatment</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#lagrangian-advection">Lagrangian Advection</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#velocity-interpolation">Velocity Interpolation</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#gradient-discretization">Gradient Discretization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#eigenvalue-solver">Eigenvalue Solver</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="#computational-density-and-comparison">Computational Density and Comparison</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#general-tips">General Tips</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="4_input.html">Input Data Files</a></li>
 <li class="toctree-l1"><a class="reference internal" href="5_gui.html">Graphical User Interface (GUI)</a></li>
 <li class="toctree-l1"><a class="reference internal" href="6_inputdeck.html">Input Deck for Solver Parameters</a></li>
@@ -81,9 +91,31 @@
 
   <section id="numerical-methods">
 <span id="numerical"></span><h1>Numerical Methods<a class="headerlink" href="#numerical-methods" title="Link to this heading"></a></h1>
+<section id="wall-treatment">
+<span id="wall"></span><h2>Wall Treatment<a class="headerlink" href="#wall-treatment" title="Link to this heading"></a></h2>
+</section>
+<section id="lagrangian-advection">
+<span id="advc"></span><h2>Lagrangian Advection<a class="headerlink" href="#lagrangian-advection" title="Link to this heading"></a></h2>
+</section>
+<section id="velocity-interpolation">
+<span id="intp"></span><h2>Velocity Interpolation<a class="headerlink" href="#velocity-interpolation" title="Link to this heading"></a></h2>
+</section>
+<section id="gradient-discretization">
+<span id="grad"></span><h2>Gradient Discretization<a class="headerlink" href="#gradient-discretization" title="Link to this heading"></a></h2>
+</section>
+<section id="eigenvalue-solver">
+<span id="eigen"></span><h2>Eigenvalue Solver<a class="headerlink" href="#eigenvalue-solver" title="Link to this heading"></a></h2>
+</section>
 </section>
 <section id="computational-density-and-comparison">
-<h1>Computational Density and Comparison<a class="headerlink" href="#computational-density-and-comparison" title="Link to this heading"></a></h1>
+<span id="numcompare"></span><h1>Computational Density and Comparison<a class="headerlink" href="#computational-density-and-comparison" title="Link to this heading"></a></h1>
+<section id="general-tips">
+<span id="numtips"></span><h2>General Tips<a class="headerlink" href="#general-tips" title="Link to this heading"></a></h2>
+<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.
+The velocity fields were interpolated with <code class="docutils literal notranslate"><span class="pre">tricubic-FL</span></code> by them, originating from <span id="id1">[Lekien2005]</span>, which has higher performance by solving a 64*64 linear system using the function values, gradients, and mixed partial derivatives at its eight corners, which is in future development plan for <code class="docutils literal notranslate"><span class="pre">Py3DFTLE</span></code> with high priority.
+Although not 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.</p>
+<p>Please always notice that, although providing much better numerical precision and looks cool in papers, high-order methods could be resource-consuming, even several hundred times.</p>
+</section>
 </section>
 
 

.doctrees/environment.pickle

@@ -3,5 +3,56 @@
 Numerical Methods
 ===================
 
+
+.. _wall:
+
+Wall Treatment
+~~~~~~~~~~~~~~~
+
+
+
+.. _advc:
+
+Lagrangian Advection
+~~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _intp:
+Velocity Interpolation
+~~~~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _grad:
+Gradient Discretization
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _eigen:
+Eigenvalue Solver
+~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _numcompare:
+
 Computational Density and Comparison
-==========================================
+==========================================
+
+.. _numtips:
+
+General Tips
+~~~~~~~~~~~~~~~~
+
+
+As for your reference, and configured as defaults, the *Berkeley LCS Tutorials* used ``RK4`` for advection.
+The velocity fields were interpolated with ``tricubic-FL`` by them, originating from [Lekien2005]_, which has higher performance by solving a 64*64 linear system using the function values, gradients, and mixed partial derivatives at its eight corners, which is in future development plan for ``Py3DFTLE`` with high priority.
+Although not detailed, ``grad_order=2`` was employed by them from the equation, supposing the mesh is sufficiently refined.
+
+Please always notice that, although providing much better numerical precision and looks cool in papers, high-order methods could be resource-consuming, even several hundred times.

3_numerical.html

@@ -113,8 +113,18 @@ <h2>Table of Contents<a class="headerlink" href="#table-of-contents" title="Link
 <li class="toctree-l2"><a class="reference internal" href="2_theory.html#unsteady-lcs">Unsteady LCS</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="3_numerical.html">Numerical Methods</a></li>
-<li class="toctree-l1"><a class="reference internal" href="3_numerical.html#computational-density-and-comparison">Computational Density and Comparison</a></li>
+<li class="toctree-l1"><a class="reference internal" href="3_numerical.html">Numerical Methods</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="3_numerical.html#wall-treatment">Wall Treatment</a></li>
+<li class="toctree-l2"><a class="reference internal" href="3_numerical.html#lagrangian-advection">Lagrangian Advection</a></li>
+<li class="toctree-l2"><a class="reference internal" href="3_numerical.html#velocity-interpolation">Velocity Interpolation</a></li>
+<li class="toctree-l2"><a class="reference internal" href="3_numerical.html#gradient-discretization">Gradient Discretization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="3_numerical.html#eigenvalue-solver">Eigenvalue Solver</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="3_numerical.html#computational-density-and-comparison">Computational Density and Comparison</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="3_numerical.html#general-tips">General Tips</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="4_input.html">Input Data Files</a></li>
 <li class="toctree-l1"><a class="reference internal" href="5_gui.html">Graphical User Interface (GUI)</a></li>
 <li class="toctree-l1"><a class="reference internal" href="6_inputdeck.html">Input Deck for Solver Parameters</a><ul>