A low-diffusion self-adaptive flux-vector splitting approach for compressible flows

David Iampietro (1) , Frédéric Daude (2) , Pascal Galon (2) , Jean-Marc Hérard (3)

1 I2M - Institut de Mathématiques de Marseille
2 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
3 EDF - EDF

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.

Mots clés: Euler equations; Flux-Vector Splitting; Low-Mach number flows; Stationary incompressible flows; Operator kernel

Domaines: Physique mathématique [math-ph]

David Iampietro, Frédéric Daude, Pascal Galon, Jean-Marc Hérard. A low-diffusion self-adaptive flux-vector splitting approach for compressible flows. 2018. ⟨hal-01945480v1⟩