A discontinuous Galerkin method for inviscid low Mach number flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Bassi, F.²  De Bartolo, C.¹  Hartmann, R.³  Nigro, A.¹ 

[1] Univ Calabria, Dipartimento Meccan, I-87036 Arcavacata Di Rende, CS, Italy

[2] Univ Bergamo, Dip Ingn Ind, I-24044 Dalmine, BG, Italy

[3] German Aerosp Ctr DLR, Inst Aerodynam & Flow Technol, D-38108 Braunschweig, Germany

关键词: Low Mach number flows;    Discontinuous Galerkin finite element method;    Preconditioning;    Euler equations;    Compressible flows;    Roe scheme;   

DOI  :  10.1016/j.jcp.2009.02.021

来源: Elsevier

【 摘 要 】

In this work we extend the high-order discontinuous Galerkin (DG) finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free