A Discontinuous Galerkin Method in Moving Domains
We present a matrix-free discontinuous Galerkin method for simulating compressible viscous flows in two- and three-dimensional moving domains in an Arbitrary Lagrangian Eulerian (ALE) framework. Spatial discretization is based on standard structured and unstructured grids but using an orthogonal spectral hierarchical basis. The method is third-order accurate in time, and converges exponentially fast in space for smooth solutions. We also report on open issues related to quadrature crimes and over-integration.
KeywordsDiscontinuous Galerkin Method Vortex Tube Arbitrary Lagrangian Eulerian Spectral Element Method Grid Velocity
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- 6.G. Di Battista, P. Eades, R. Tamassia, and I.G. Tollis. Graph Drawing. Prentice Hall, 1998.Google Scholar
- 10.L.-W. Ho. A Legendre spectral element method for simulation of incompressible unsteady free-surface flows. PhD thesis, Massachustts Institute of Technology, 1989.Google Scholar
- 11.B. Koobus and C. Farhat. Second-order schemes that satisfy GCL for flow computations on dynamic grids. In AIAA 98–0113, 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 12–15, 1998.Google Scholar
- 12.G.E. Karniadakis and S.J. Sherwin. Spectral/hp Element Methods for CFD. Oxford University Press, 1999.Google Scholar
- 14.I. Lomtev, R.M. Kirby, and G.E. Karniadakis. A discontinuous Galerkin ALE method for viscous compressible flows in moving domains. J. Comp. Phys., to appear, 1999.Google Scholar
- 18.G. Karypis and V. Kumar. METIS: Unstructured graph partitioning and sparse matrix orderingsystem version 2.0. Technical report, Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, 1995.Google Scholar