Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation. (English) Zbl 1129.76030

Hartmann, Ralf; Houston, Paul

Int. J. Numer. Anal. Model. 3, No. 1, 1-20 (2006).

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 theory)

Keywords:

Newton-GMRES algorithm; a posteriori error estimation

Software:

deal.ii; HE-E1GODF