Summary
We deal with the numerical solution of the compressible Navier-Stokes equations with the aid of the discontinuous Galerkin finite element (DG FE) approach with the nonsymmetric interior penalty terms. The linearization of diffusive terms and the treatment of the boundary conditions are discussed. Several numerical examples demonstrating the efficiency of the numerical method are presented.
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Bassi, F., Rebay, S.(1997): A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys, 131, 267–279
Bassi, F., Rebay, S.(2000): A high order discontinuous Galerkin method for compressible turbulent flow. In Cockburn, B., Karniadakis, G. E., Shu, C.-W. (eds) Discontinuous Galerkin Method: Theory, Computations and Applications, Lecture Notes in Computational Science and Engineering 11, pages 113–123. Springer-Verlag
Bristeau, M. O., Glowinski, R., Periaux, J., Viviand, H. eds (1987): Numerical Simulation of Compressible Navier-Stokes Flows, volume 18 of Notes on Numerical Fluid Mechanics. Vieweg, Braunschwig
Cockburn B. (1999): Discontinuous Galerkin methods for convection dominated problems. In Barth, T.J., Deconinck, H., (eds), High-Order Methods for Computational Physics, Lecture Notes in Computational Science and Engineering 9, pages 69–224. Springer, Berlin
Cockburn, B., Karniadakis, G. E., Shu, C.-W. eds (2000) Discontinuous Galerkin methods. Lecture Notes in Computational Science and Engineering 11., Springer, Berlin
Dolejší, V. (2002): A higher order scheme based on the finite volume approach. In R. Herbin and D. Kröner, (eds), Finite Volumes for Complex Applications III (Problems and Perspectives), pages 333–340. Hermes
Dolejší, V.: On the discontinuous Galerkin method for the numerical solution of the Navier-Stokes equations. Int. J. Numer. Methods Fluids, (submitted)
Dolejší, V., Feistauer, M., Sobotíkovä, V.: A discontinuous Galerkin method for nonlinear convection-diffusion problems. Comput. Methods Appl. Mech. Eng. (submitted)
Feistauer, M., Felcman, J., Straškraba, I. (2003): Mathematical and Computational Methods for Compressible Flow. Oxford University Press, Oxford
Toro, E.F. (1997): Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag
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Dolejší, V. (2004). Discontinuous Galerkin Finite Element Method for the Numerical Solution of Viscous Compressible Flows. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_23
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DOI: https://doi.org/10.1007/978-3-642-18775-9_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62288-5
Online ISBN: 978-3-642-18775-9
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