StroemungsRaum#

StroemungsRaum is a research software project developed within the BMFTR-funded project

“StrömungsRaum – Novel Exascale Architectures with Heterogeneous Hardware Components for Computational Fluid Dynamics Simulations” (October 2022 – September 2025).

The project addresses the development of scalable numerical methods and high-performance algorithms for Computational Fluid Dynamics (CFD) targeting future exascale computing architectures with heterogeneous hardware.

Scope of This Repository#

This repository contains the Forschungszentrum Jülich (FZJ) contribution to the StrömungsRaum project, focusing on:

  • Parallel-in-time methods

  • Combined space–time parallelization for fluid simulations

  • Algorithmic scalability for time-dependent PDEs

The goal is to expose concurrency beyond spatial parallelism and enable efficient execution on large-scale HPC systems.

Model Problems and Methods#

Implemented examples and test cases include:

  • Heat equation

  • Convection–diffusion and nonlinear convection–diffusion problems

  • Incompressible Navier–Stokes equations, using:

    • Projection methods

    • Monolithic formulations

    • DAE- and PDE sweepers

These serve as benchmarks and demonstrators for scalable space–time CFD simulations.

Order reduction from time-dependent boundary conditions#

run_Navier_Stokes_TaylorGreen_FEniCS.py runs a manufactured Taylor–Green solution on \([-0.5, 0.5]^2\) that is exactly one-periodic in \(x\) and constant on the top and bottom boundary. The same solution can therefore be computed with time-dependent Dirichlet conditions in \(x\) or with periodic ones, and the difference in the observed temporal order isolates the order reduction caused by the time-dependent boundary data alone.

The number of collocation nodes decides whether the effect is visible: RADAU-RIGHT with \(M\) nodes drops from its design order \(2M-1\) to the stiff order \(M+1\), so the gap is \(M-2\) and vanishes for \(M = 2\). With \(M = 4\) the measured pressure orders are 7 with periodic and 5 with time-dependent Dirichlet conditions.

The third variant, differentiated_bc, imposes the boundary data on its time derivative and recovers the stage values by collocation quadrature instead of evaluating the data pointwise at the nodes. This is the boundary-condition analogue of the differentiated-constraint remedy explored in pull request #641, and it removes most of the penalty: at \(M = 4\) the pressure error drops by roughly an order of magnitude, to within a small factor of the periodic case.

Funding#

Funded by the German Federal Ministry of Research, Technology and Space (BMFTR) under grant number 16ME0708.