A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes

In this paper a new hybrid semi-implicit finite volume / element (FV/FE) scheme is presented for the numerical solution of compressible Euler and Navier–Stokes equations at all Mach numbers on unstructured staggered meshes in two three space dimensions. The chosen grid arrangement consists primal simplex mesh composed triangles or tetrahedra, an edge-based face-based dual mesh. governing are discretized conservation form. nonlinear convective terms equations, as well viscous stress tensor heat flux, aid explicit local ADER scheme, while implicit pressure continuous P1 method nodes zero number limit, automatically reduces to FV/FE approach forwarded [1] incompressible equations. As such, asymptotically consistent with limit can therefore be applied flows numbers. Due discretization, CFL restriction time step only based magnitude flow velocity not sound speed, hence computationally efficient low unknown scalar field step. Furthermore, resulting system symmetric positive definite very efficiently solved matrix-free conjugate gradient method. order assess capabilities we show computational results large set benchmark problems that range from quasi regime shock waves.