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‎.doctrees/1_requirements.doctree‎

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‎.doctrees/3_numerical.doctree‎

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‎1_requirements.html‎

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@@ -97,11 +97,10 @@ <h2>Hardware and Hardware Requirements<a class="headerlink" href="#hardware-and-
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<p>GPU acceleration is suggested for large dataset computation. Therefore, the requirements for GPU acceleration is listed as follows:</p>
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<ul class="simple">
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<li><p>NVIDIA GPUs, with a minimum <a class="reference external" href="https://developer.nvidia.com/cuda-gpus">compute capability</a> of 5.0, i.e., later than GTX 750.</p></li>
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<li><p>It is suggested that, make <code class="docutils literal notranslate"><span class="pre">Nx</span></code> × <code class="docutils literal notranslate"><span class="pre">Ny</span></code> × <code class="docutils literal notranslate"><span class="pre">Nz</span></code> × <code class="docutils literal notranslate"><span class="pre">Nt</span></code> less than 200,000,000 Lagrangian particles on each Gigabyte of GPU memory for double-side computation under default numerical methods for one still. Generally half it under high-order computations.</p></li>
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<li><p>It is suggested that, make <code class="docutils literal notranslate"><span class="pre">Nx</span></code> × <code class="docutils literal notranslate"><span class="pre">Ny</span></code> × <code class="docutils literal notranslate"><span class="pre">Nz</span></code> × <code class="docutils literal notranslate"><span class="pre">Nt</span></code> less than 200,000,000 Lagrangian particles on each Gigabyte of GPU memory for double-side computation under default numerical methods for one still. Generally half it under high-order computations. For example, you can execute on a 600×300×300 mesh for c.a. 80 time steps for a still on a welcomed RTX 2080ti 22G customized GPU, with the price of ~$400.</p></li>
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<li><p>The general short for GPU is VRAM, not computational power, hence old-but-large GPUs are great for use. Newers can be faster, but smallers can run nothing.</p></li>
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<li><p>The GPU requirements for dynamic LCS are undergoing experiments by the author.</p></li>
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</ul>
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<p>For example, you can execute on a 600×300×300 mesh for c.a. 80 time steps for a still on a welcomed RTX 2080ti 22G customized GPU, with the price of ~$400.
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* The general short for GPU is VRAM, not computational power, hence old-but-large GPUs are great for use. Newers can be faster, but smallers can run nothing.
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* The GPU requirements for dynamic LCS are undergoing experiments by the author.</p>
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</section>
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<section id="basic-environment">
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<h2>Basic Environment<a class="headerlink" href="#basic-environment" title="Link to this heading"></a></h2>
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</section>
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<section id="quickstart">
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<h2>Quickstart<a class="headerlink" href="#quickstart" title="Link to this heading"></a></h2>
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<p>An computation example coming with a set of our in-house downscaled Direct Navier-Stokes Simulation (DNS) data is provided, including :math:
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<p>After configurations of environment, you can run a very first demo to test the environment as well as the code, and learn how to use this toolbox for your own data towards new insights.
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An computation example coming with a set of our in-house downscaled Direct Navier-Stokes Simulation (DNS) data is provided, including :math:
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The dataset can be downloaded from <a class="reference external" href="https://noting.noting">here</a>, and the case descriptions can be referred to paper <code class="docutils literal notranslate"><span class="pre">I.P.</span></code>.</p>
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</section>
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</section>

‎3_numerical.html‎

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k_6 = \mathbf{u}\!\bigl(\mathbf{x}_n + \Delta t(-\tfrac{3}{2}k_1 + 2k_2 - \tfrac{1}{2}k_3 + k_4),\;t_n + \Delta t\bigr),\\
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\mathbf{x}_{n+1} = \mathbf{x}_n + \Delta t\bigl(\tfrac{1}{20}k_1 + \tfrac{1}{4}k_4 + \tfrac{1}{5}k_5 + \tfrac{1}{2}k_6\bigr).\end{split}\]</div>
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<p>This scheme incurs a global error of order <span class="math notranslate nohighlight">\(O(\Delta t^6)\)</span> with six velocity evaluations.</p>
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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><code class="docutils literal notranslate"><span class="pre">output_dir</span></code></p></th>
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<th class="head"><p>Path to directory for saving results</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">&lt;string&gt;</span></code></p></th>
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<th class="head"></th>
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</tr>
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<tr class="row-even"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">auto_wall</span></code></p></th>
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<th class="head"><p>Flag for automatic wall detection</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">0</span></code></p></th>
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<th class="head"><p>Manually indicate computation bounds.</p></th>
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</tr>
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<tr class="row-odd"><th class="head"></th>
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<th class="head"></th>
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<th class="head"><p>(<code class="docutils literal notranslate"><span class="pre">1</span></code>)</p></th>
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<th class="head"><p>Auto detect bounds from input mesh.</p></th>
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</tr>
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<tr class="row-even"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">wall_xrange</span></code></p></th>
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<th class="head"><p>X-direction wall bounds [xmin, xmax]</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">[&lt;float&gt;,</span> <span class="pre">&lt;float&gt;]</span></code></p></th>
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<th class="head"><p>Dimensionalized coordinates bounds.</p></th>
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</tr>
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<tr class="row-odd"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">wall_yrange</span></code></p></th>
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<th class="head"><p>Y-direction wall bounds [ymin, ymax]</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">[&lt;float&gt;,</span> <span class="pre">&lt;float&gt;]</span></code></p></th>
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<th class="head"></th>
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</tr>
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<tr class="row-even"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">wall_zrange</span></code></p></th>
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<th class="head"><p>Z-direction wall bounds [zmin, zmax]</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">[&lt;float&gt;,</span> <span class="pre">&lt;float&gt;]</span></code></p></th>
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<th class="head"></th>
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</tr>
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<tr class="row-odd"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">x</span></code></p></th>
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<th class="head"><p>Number of Lagrangian seed points in X direction</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">&lt;int&gt;</span></code></p></th>
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<th class="head"></th>
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</tr>
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<tr class="row-even"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">y</span></code></p></th>
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<th class="head"><p>Number of Lagrangian seed points in Y direction</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">&lt;int&gt;</span></code></p></th>
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<th class="head"></th>
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</tr>
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<tr class="row-odd"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">z</span></code></p></th>
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<th class="head"><p>Number of Lagrangian seed points in Z direction</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">&lt;int&gt;</span></code></p></th>
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<th class="head"></th>
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</tr>
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<tr class="row-even"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">T_range</span></code></p></th>
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<th class="head"><p>Time range [<code class="docutils literal notranslate"><span class="pre">T_start</span></code>, <code class="docutils literal notranslate"><span class="pre">T_end</span></code>] in frames</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">[&lt;float&gt;,</span> <span class="pre">&lt;float&gt;]</span></code></p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">T_end</span></code> no larger than <code class="docutils literal notranslate"><span class="pre">N_frames</span></code>.</p></th>
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</tr>
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<tr class="row-odd"><th class="head"><p><code class="docutils literal notranslate"><span class="pre">dt</span></code></p></th>
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<th class="head"><p>Time step for particle advection in frames</p></th>
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<th class="head"><p><code class="docutils literal notranslate"><span class="pre">&lt;float&gt;</span></code></p></th>
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<th class="head"></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">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><p>Perform physical advection.</p></td>
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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>
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<section id="ftle-computation">

‎_sources/1_requirements.rst.txt‎

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GPU acceleration is suggested for large dataset computation. Therefore, the requirements for GPU acceleration is listed as follows:
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* NVIDIA GPUs, with a minimum `compute capability <https://developer.nvidia.com/cuda-gpus>`__ of 5.0, i.e., later than GTX 750.
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* It is suggested that, make ``Nx`` × ``Ny`` × ``Nz`` × ``Nt`` less than 200,000,000 Lagrangian particles on each Gigabyte of GPU memory for double-side computation under default numerical methods for one still. Generally half it under high-order computations.
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For example, you can execute on a 600×300×300 mesh for c.a. 80 time steps for a still on a welcomed RTX 2080ti 22G customized GPU, with the price of ~$400.
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* It is suggested that, make ``Nx`` × ``Ny`` × ``Nz`` × ``Nt`` less than 200,000,000 Lagrangian particles on each Gigabyte of GPU memory for double-side computation under default numerical methods for one still. Generally half it under high-order computations. For example, you can execute on a 600×300×300 mesh for c.a. 80 time steps for a still on a welcomed RTX 2080ti 22G customized GPU, with the price of ~$400.
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* The general short for GPU is VRAM, not computational power, hence old-but-large GPUs are great for use. Newers can be faster, but smallers can run nothing.
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* The GPU requirements for dynamic LCS are undergoing experiments by the author.
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Quickstart
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-----------------
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After configurations of environment, you can run a very first demo to test the environment as well as the code, and learn how to use this toolbox for your own data towards new insights.
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An computation example coming with a set of our in-house downscaled Direct Navier-Stokes Simulation (DNS) data is provided, including :math:
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The dataset can be downloaded from `here <https://noting.noting>`__, and the case descriptions can be referred to paper ``I.P.``.

‎_sources/3_numerical.rst.txt‎

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This scheme incurs a global error of order :math:`O(\Delta t^6)` with six velocity evaluations.
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``output_dir`` | Path to directory for saving results | ``<string>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``auto_wall`` | Flag for automatic wall detection | ``0`` | Manually indicate computation bounds. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| | | (``1``) | Auto detect bounds from input mesh. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``wall_xrange`` | X-direction wall bounds [xmin, xmax] | ``[<float>, <float>]`` | Dimensionalized coordinates bounds. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``wall_yrange`` | Y-direction wall bounds [ymin, ymax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``wall_zrange`` | Z-direction wall bounds [zmin, zmax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``x`` | Number of Lagrangian seed points in X direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``y`` | Number of Lagrangian seed points in Y direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``z`` | Number of Lagrangian seed points in Z direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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| ``T_range`` | Time range [``T_start``, ``T_end``] in frames | ``[<float>, <float>]`` | ``T_end`` no larger than ``N_frames``. |
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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>`` | Perform physical advection. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------------------------------------------------------+
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.. _ftlefinal:
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FTLE Computation

‎searchindex.js‎

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