Computational PDEs

Computational Fluid Dynamics(CFD) on HPC for (indoor air) flows

The physical problem.

Starting point are the incompressible Navier-Stokes equation for a velocity \(u\) and pressure \(p\) solving \begin{align} \partial_t u - \operatorname{Re}^{-1} \Delta u + \operatorname{div}( u \otimes u ) - \nabla p & = f, \\ \operatorname{div}( u ) & = 0, \end{align} The problematic case with the incompressible Navier-Stokes equations considered here is the high Reynolds number situation which forbids the resolution of all relevant scales that may appear in a flow. In this project a Large Eddy Simulation (LES) shall be implemented, where only a certain amount of scales can be resolved, but the effect of smaller scales on the resolvable scales is modeled properly, here using a Variational Multiscale (VMS) approach.

\(H(\operatorname{div})\)-conforming HDG discretization for incompressible flows

In this project we want to consider the \(H(\operatorname{div})\)-conforming HDG discretization which is known to also be a valid implicit LES discretization, cf. e.g. [FKL+19].

Peter Vogel room

We want to simulate a specific configuration, the so-called Peter-Vogel room which is an academic examples with existing measurements. Details will be provided.

Tasks

  • Familiarize with the \(H(\operatorname{div})\)-conforming HDG discretization, e.g. the version implemented in NGSolve model templates.
  • Familiarize with the HPC cluster of the GWDG and slurm.
  • Setup the Peter Vogel configuration and carry out simulations for different Reynolds numbers (multicore with and without MPI).
  • Evaluate and profile the simulation runs
  • Switch to the VMS model (when finished) and compare results

References

[1] GWDG HPC getting started

[2] GWDG HPC wiki

[3] GWDG HPC cluster introduction

[4] NGSolve's i-tutorials on basic MPI usage with NGSolve

[5] NGSolve's i-tutorials on dof organisation for MPI-parallel NGSolve

[6] NGSolve's i-tutorials on converting NGSolve's linear algebra objects to PETSc objects

[7] NGSolve's i-tutorials on convenience functionality for converting NGSolve's linear algebra objects to PETSc objects