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Discontinuous Galerkin Method for the Numerical Solution of Inviscid and Viscous Compressible Flow

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • V. Kučera

    (Charles University in Prague, Faculty of Mathematics and Physics)

Abstract

In this work we are concerned with the numerical solution of a viscous compressible gas flow (compressible Navier-Stokes equations) with the aid of the discontinuous Galerkin finite element method (DGFEM). Our goal is to incorporate viscous terms into existing semi-implicit DGFEM scheme for the Euler equations, which is capable of solving flows with a wide range of Mach numbers [2, 4]. The nonsymmetric (NIPG), symmetric (SIPG) and incomplete interior penalty Galerkin method (IIPG) are generalized using the unified framework of [1] – derived for the Poisson equation – to the Navier-Stokes viscous terms. The resulting nonlinearities are linearized in a similar manner as nonlinear convective terms in the original scheme, thus enabling semi-implicit time stepping. The resulting scheme has very good stability properties and requires the solution of one sparse linear system per time level.

Suggested Citation

  • V. Kučera, 2008. "Discontinuous Galerkin Method for the Numerical Solution of Inviscid and Viscous Compressible Flow," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 339-346, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_40
    DOI: 10.1007/978-3-540-69777-0_40
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