Colloquium

A high-performance second-order collocation-type finite-element scheme for solving the compressible Navier-Stokes equations on unstructured meshes is presented. The method uses Strang splitting, is second-order accurate in time and space, and is based on a convex limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211-A3239, 2018). As such it is invariant-domain preserving, meaning, the solver maintains important physical invariants and is guaranteed to be stable without the use of ad-hoc tuning parameters.
In this talk I will introduce the discretization technique, discuss the convex limiting approach and algorithmic design of the method, and comment on a high-performance implementation utilizing SIMD (single instruction multiple data) vectorization.
This is joint work with Jean-Luc Guermond, Martin Kronbichler, Bojan Popov, Ignacio Tomas