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

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 it produces results that are reproducible and that can be shown to be accurate on challenging 2D and 3D realistic benchmarks.