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Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation. (English) Zbl 1129.76030
Summary: We consider discontinuous Galerkin finite element methods for numerical approximation of compressible Navier-Stokes equations. For discretization of the leading order terms, we propose a generalization of the symmetric version of interior penalty method, originally developed for numerical approximation of linear self-adjoint second-order elliptic partial differential equations. In order to solve the resulting system of nonlinear equations, we exploit a (damped) Newton-GMRES algorithm. Numerical experiments demonstrate the practical performance of the proposed discontinuous Galerkin method with higher-order polynomials.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics, general
Software:
deal.ii; HE-E1GODF
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