A low-diffusion self-adaptive flux-vector splitting approach for compressible flows. (30th June 2020) - Iampietro, D.; Daude, F.; Galon, P.
Highlights: Flux vector splitting methods allow to separate convection and acoustic operators. Adaptive splitting adapts space discretization in order to capture a wide range of Mach number regimes. Godunov-like schemes applied to acoustic operators provide appropriate upwind discretizations for velocity and pressure. Low-Mach corrections should be applied on the momentum and the energy equation. Abstract: A low-diffusion self-adaptive flux-vector splitting method is presented for the Euler equations. The flux-vector is here split into convective and acoustic parts following the formulation recently proposed by the authors. This procedure is based on the Zha-Bilgen (or previously Baraille et al. for the Euler barotropic system) approach enriched by a dynamic flow-dependent splitting parameter based on the local Mach number. As a consequence, in the present self-adaptive splitting, the convective and acoustic parts decouple in the low-Mach number regime whereas the complete Euler equations are considered for the sonic and highly subsonic regimes. The low diffusive property of the present scheme is obtained by adding anti-diffusion terms to the momentum and the energy components of the pressure flux in the acoustic part of the present splitting. This treatment results from a formal invariance principle preserving the discrete incompressible phase space through the pressure operator. Numerical results for several carefully chosen one- and two-dimensional test problems are finally investigated to demonstrate the accuracy and robustness of the proposed scheme for a wide variety of configurations from subsonic to highly subsonic flows.