deploy: a7ff60f

Author: hweifluids

.doctrees/6_inputdeck.doctree

@@ -236,7 +236,7 @@ <h2>Numerical Methods<a class="headerlink" href="#numerical-methods" title="Link
 <tr class="row-odd"><td></td>
 <td></td>
 <td><p>(<code class="docutils literal notranslate"><span class="pre">tricubic</span></code>)</p></td>
-<td></td>
+<td><p>Catmull–Rom 3D convolution kernel.</p></td>
 </tr>
 <tr class="row-even"><td></td>
 <td></td>
@@ -248,39 +248,46 @@ <h2>Numerical Methods<a class="headerlink" href="#numerical-methods" title="Link
 <td><p><code class="docutils literal notranslate"><span class="pre">WENO</span></code></p></td>
 <td><p>Weighted Essentially Non-Oscillatory (WENO) scheme with shockwave capture capability.</p></td>
 </tr>
-<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">grad_order</span></code></p></td>
+<tr class="row-even"><td></td>
+<td></td>
+<td><p>(<code class="docutils literal notranslate"><span class="pre">tricubic-FL</span></code>)</p></td>
+<td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> The high-performance 3D tricubic interpolation method by <span id="id1">[Lekien2005]</span>.</p></td>
+</tr>
+<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">grad_order</span></code></p></td>
 <td><p>The method (order) of gradient discretization</p></td>
 <td><p>(<code class="docutils literal notranslate"><span class="pre">2</span></code>)</p></td>
 <td><p>2nd-order central difference.</p></td>
 </tr>
-<tr class="row-odd"><td></td>
+<tr class="row-even"><td></td>
 <td></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">4</span></code></p></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> 4th-order central difference.</p></td>
 </tr>
-<tr class="row-even"><td></td>
+<tr class="row-odd"><td></td>
 <td></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">6</span></code></p></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> 6th-order central difference.</p></td>
 </tr>
-<tr class="row-odd"><td></td>
+<tr class="row-even"><td></td>
 <td></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">100</span></code></p></td>
 <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>
 </tr>
-<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">Eigen_method</span></code></p></td>
+<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">eigen_method</span></code></p></td>
 <td><p>Solver for max eigenvalue of Cauchy–Green tensor</p></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">eigmax_sym3</span></code></p></td>
 <td><p>Closed-form cubic eigenvalue solver for symmetric 3×3 matrices (noniterative solver).</p></td>
 </tr>
-<tr class="row-odd"><td></td>
+<tr class="row-even"><td></td>
 <td></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">jacobi</span></code></p></td>
 <td><p><code class="docutils literal notranslate"><span class="pre">I.P.</span></code> Jacobi eigenvalue algorithm (iterative).</p></td>
 </tr>
 </tbody>
 </table>
-<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.
+<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 by <code class="docutils literal notranslate"><span class="pre">tricubic-FL</span></code>, originating from <span id="id2">[Lekien2005]</span>, which has higher performance from
+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.
 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>
 </section>
 <section id="dynamic-lcs-window">

.doctrees/environment.pickle

@@ -65,12 +65,14 @@ Numerical Methods
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 | ``interp_method`` | Interpolation method for velocity fields             | ``trilinear``           | Simple and fast triliear interpolation method. Very fast on GPUs.                                       |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
-|                   |                                                      | (``tricubic``)          |                                                                                                         |
+|                   |                                                      | (``tricubic``)          | Catmull–Rom 3D convolution kernel.                                                                      |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 |                   |                                                      | ``hermite``             |                                                                                                         |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 |                   |                                                      | ``WENO``                | Weighted Essentially Non-Oscillatory (WENO) scheme with shockwave capture capability.                   |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
+|                   |                                                      | (``tricubic-FL``)       | ``I.P.`` The high-performance 3D tricubic interpolation method by [Lekien2005]_.                        |
++-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 | ``grad_order``    | The method (order) of gradient discretization        | (``2``)                 | 2nd-order central difference.                                                                           |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 |                   |                                                      | ``4``                   | ``I.P.`` 4th-order central difference.                                                                  |
@@ -79,12 +81,14 @@ Numerical Methods
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 |                   |                                                      | ``100``                 | ``I.P.`` Global Fast Fourier Transform (FFT) with finite order. Compute extremely intensive!            |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
-| ``Eigen_method``  | Solver for max eigenvalue of Cauchy–Green tensor     | ``eigmax_sym3``         | Closed-form cubic eigenvalue solver for symmetric 3×3 matrices (noniterative solver).                   |
+| ``eigen_method``  | Solver for max eigenvalue of Cauchy–Green tensor     | ``eigmax_sym3``         | Closed-form cubic eigenvalue solver for symmetric 3×3 matrices (noniterative solver).                   |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 |                   |                                                      | ``jacobi``              | ``I.P.`` Jacobi eigenvalue algorithm (iterative).                                                       |
 +-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
 
-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.
+As for your reference, and configured as defaults, the *Berkeley LCS Tutorials* used ``RK4`` for advection.
+The velocity fields were interpolated by ``tricubic-FL``, originating from [Lekien2005]_, which has higher performance from 
+Although non 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 hundreds of times.
 
 Dynamic LCS Window