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

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.
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Submitted on : Tuesday, December 18, 2018 - 4:46:46 PM
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David Iampietro, Frédéric Daude, Pascal Galon. A low-diffusion self-adaptive flux-vector splitting approach for compressible flows. Computers and Fluids, Elsevier, 2020, 206(C), ⟨10.1016/j.compfluid.2020.104586⟩. ⟨hal-01945480v2⟩



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