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

• Published in: Computer methods in applied mechanics and engineering 2022-02, Vol.389, p.114250, Article 114250
• Main Authors: Guermond, Jean-Luc, Kronbichler, Martin, Maier, Matthias, Popov, Bojan, Tomas, Ignacio
• Format: Article
• Language: English
• Subjects: Beräkningsvetenskap; Compressibility; compressible Navier–Stokes equations; Convex limiting; Finite element method; Fluid flow; High-order method; Hyperbolic conservation equations; Invariant domains; Mathematical analysis; Navier-Stokes equations; Robustness; Scientific Computing
• ISSN: 0045-7825; 1879-2138; 1879-2138
• DOI: 10.1016/j.cma.2021.114250

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. •Second-order accurate Finite element solver for the compressible Navier-Stokes equations.•Provable invariant-domain preservation under the hyperbolic CFL time step restriction.•Detailed treatment of robust, invariant-domain preserving boundary conditions.•Demonstrated accuracy and scalability of the method on parallel computer architectures.•Source code and test vectors have been made available to allow comparison of methods.