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3 results for “Navier-Stokes equations”
Convolutional Neural Networks for LPV-Approximations of Semi-discrete Navier-Stokes Equations
<pre><code>A `python` module with * a dynamic setup of *Convolutional Neural Networks* in `PyTorch` * an interface to `FEniCS` to generate data from FEM simulations of flows and * a numerical realization of FEM norm in the training neural networks developed to design very low-dimensional LPV approximations of incompressible Navier-Stokes equations.</code></pre> <p> </p> <p><code>These files contain the core module </code>and the scripts that produce the numerical examples of the paper with <a href="https://doi.org/10.3389/fams.2022.879140">doi:10.3389/fams.2022.879140</a></p> <p> </p> <pre><code>> Benner, Heiland, Bahmani (2022): *Convolutional Neural Networks for Very Low-dimensional LPV Approximations of Incompressible Navier-Stokes Equations* </code></pre> <p> </p>
Files for "On exactly incompressible DG FEM pressure splitting schemes for the Navier-Stokes equation"
<p>Input files and scripts sufficient to reproduce the results shown in the paper "On exactly incompressible DG FEM pressure splitting schemes for the Navier-Stokes equation".</p> <p>A version of Ocellaris similar to version 2019.0.1 was used and all results should be reproducible by this version of Ocellaris. See <a href="https://bitbucket.org/ocellarisproject/ocellaris/">the Ocellaris source code repository</a>, <a href="https://pypi.org/project/ocellaris/2019.0.1/">Ocellaris 2019.0.1 on PyPi</a>, or DOI <a href="https://zenodo.org/record/2558303">10.5281/zenodo.2558303</a>.</p> <p>The Ocellaris user guide can be found at <a href="https://www.ocellaris.org">www.ocellaris.org</a> and it includes guides to how to run Ocellaris in Singularity or Docker containers for ease of installation and testing. Containers for Ocellaris 2019.0.0 are available, for Docker run:</p> <pre><code class="language-bash"># On the host machine: docker run -it trlandet/fenics-dev:2018.1.0.r3 # Inside the Docker container pip3 install ocellaris==2019.0.1 --user </code></pre> <p> </p>
Navier-Stokes Extension Equation
<p>The Navier-Stokes Extension Equation enhances the classical Navier-Stokes equations by incorporating explicit smoothness conditions, , ensuring no physical singularities and guaranteeing stable solutions for real-world flow problems. The fundamental equation is:</p> <p> </p> <p><strong>\rho \frac{\partial u}{\partial t} + \rho (u \cdot \nabla) u = - \nabla p + \mu \Delta u</strong></p> <p> </p> <p>This describes the dynamics of incompressible fluids, addressing pressure gradients, viscosity, and mass conservation (). It is applicable in fields such as meteorology, astrophysics, and biomechanics, providing stable and precise flow simulations.</p>
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