On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations

TL;DR

This paper presents a robust, efficient finite element-based parallel solver for the compressible Navier-Stokes equations, demonstrating high accuracy and reproducibility on complex 2D and 3D benchmarks.

Contribution

It introduces a provably robust finite element method that is invariant domain preserving and optimized for modern hardware, with detailed implementation insights.

Findings

Achieves second-order accuracy in time and space

Proves invariance domain preservation under CFL restriction

Demonstrates excellent performance on realistic benchmarks

Abstract

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is second-order accurate in time and space. Robustness here means that the method is proved to be invariant domain preserving under the hyperbolic CFL time step restriction, and the method delivers results that are reproducible. The proposed technique is shown to be accurate on challenging 2D and 3D realistic benchmarks.