Efficient parallel 3D computation of the compressible Euler equations with an invariant-domain preserving second-order finite-element scheme

TL;DR

This paper presents an efficient parallel implementation of a second-order finite-element scheme for the compressible Euler equations that preserves physical invariants and scales well on high-performance computing architectures.

Contribution

It introduces a SIMD-vectorized, invariant-domain preserving finite-element solver with optimized parallelization for gas dynamics simulations.

Findings

Achieved excellent weak and strong scaling on parallel architectures.

Developed SIMD-compatible compute kernels for high performance.

Maintained physical invariants without ad-hoc tuning.

Abstract

We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211-A3239, 2018). As such it is invariant-domain preserving, i.e., the solver maintains important physical invariants and is guaranteed to be stable without the use of ad-hoc tuning parameters. This stability comes at the expense of a significantly more involved algorithmic structure that renders conventional high-performance discretizations challenging. We develop an algorithmic design that allows SIMD vectorization of the compute kernel, identify the main ingredients for a good node-level performance, and report excellent weak and strong scaling of a hybrid thread/MPI parallelization.