A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular the approximate solution incompressible and compressible Navier-Stokes equations, as well shallow water equations on staggered unstructured meshes two three space dimensions. The key features method are use an edge-based/face-based dual mesh discretization nonlinear convective terms at aid explicit high resolution Godunov-type volume schemes, while pressure discretized implicitly using classical continuous Lagrange elements primal simplex mesh. resulting system is symmetric positive definite can thus be very efficiently solved Krylov subspace methods, such matrix-free conjugate gradient method. For by construction asymptotic preserving low Mach number limit hence consistent FV/FE retrieved. All parts algorithm parallelized, i.e., step matrix-vector product implicit solver. Concerning parallel implementation, employ Message-Passing Interface (MPI) standard combination with spatial domain decomposition based free software package METIS. To show versatility proposed present wide range applications, starting from environmental geophysical flows, dambreak problems natural convection, over direct numerical simulations turbulent flows to shock waves. An excellent agreement exact analytical, or experimental reference solutions achieved all cases. Most run millions degrees freedom thousands CPU cores. We strong scaling results scheme applied 3D up 4096 largest simulation shown paper well-known Taylor-Green vortex benchmark 671 million tetrahedral 32,768 cores, showing clearly suitability presented large CFD modern massively distributed memory supercomputers.