On the computation of steady-state compressible flows using a discontinuous Galerkin method

• Published in: International journal for numerical methods in engineering 2008-01, Vol.73 (5), p.597-623
• Main Authors: Luo, Hong, Baum, Joseph D., Löhner, Rainald
• Format: Article
• Language: English
• Subjects: compressible flows; Compressible flows; shock and detonation phenomena; Computational techniques; discontinuous Galerkin methods; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; p-multigrid; Physics; shock detectors; Shock-wave interactions and shock effects
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2081

Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd.