H(div)-based Finite Element Methods for the Navier-Stokes Equations

Joachim Schöberl
TU Wien

based on joint work with

Christoph Lehrenfeld, Georg-August-Universität Göttingen
Philip Lederer, Xaver Mooslechner, TU Wien
Jay Gopalakrishnan, Portland State University
Matthias Hochsteger, Christopher Lackner CERBSim GmbH

This presentation uses the open-source finite element library NGSolve (www.ngsolve.org) within Jupyter Notebooks.

Methods:

• Function-Space \(H(\operatorname{div})\)

• Hybrid Discontinuous Galerkin Methods

• HDG methods for Stokes

• HDG methods for Navier Stokes

• Mixed Stress-Methods for Stokes

Model templates:

• Navier Stokes

• Natural Convection

Turbulence

Parallel Solvers

Various projects

• Navier-Stokes on Surfaces

• Domain morphing

• Fluid-Structure interaction

Software design:

• NGSolve is written in modern C++, now on C++17

• Classes are ported to Python using pybind11

• MPI-based distributed memory parallelization

• C++ thread based shared memory parallelization (TaskManager)

• Python expression trees passed to C++, optional Code generation at run-time

If you like to try out this talk in your browser:

jupyterhub.cerbsim.com

user: ngshub_xx
pwd: solve!xx

xx = choose a number: 01 to 39

You find the notebooks in the shared folder.