Abstract
We consider a numerical scheme for the nonlinear Euler equations of gasdynamics in 2-D. The algorithm doesn’t use any dimensional splitting. It is a generalization of a scheme, which was developped by Roe for the linear Euler equations. In 1-D perturbations can propagate only in two directions but in 2-D there are infinite many directions of propagation. Therefore the algorithm should be able to select the most important directions and to ensure that the scheme takes this fact into account. In this paper we shall describe some details of this algorithm and we shall present some numerical results in 1-D and 2-D.
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References
P. Colella, Multidimensional upwind methods for hyperbolic conservation laws. Report Lawrence Berkeley Laboratory 17023, 1984.
S.F. Davis, A rotationally biased upwind difference scheme for the Euler equations.J.of Comp. Physics 56 (1984), 65–92.
Ch. Hirsch, C. Lacor, H. Deconinck, Convection algorithm on a diagonal procedure for the multidimensional Euler equation. AIAA, Proceedings of the 8-th Computational Fluid Dynamics Conference 1987.
R.J. LeVeque, High resolution finite volume methods on grids via wave propagation. ICASE REPORT NO.87–68, 1987
R.J. LeVeque, Cartesian grid methods for flow in irregular regions. To appear in the Proceedings of the Oxford Conference on Numerical Methods in Fluid Dynamics, 1988.
P. Roe, A basis for upwind differentiating of the two dimensional unsteady Euler equations. Numerical methodes for fluid dynamics II, Eds.: Morton, Baines, Oxford Univ. Press 1986.
P. Roe, Discrete models for the numerical analysis of time dependent multidimensional gas dynamics. Icase report 85–18,1985.
P. Roe, Approximate Riemann solvers, parameter vectors difference schemes. J.of Comp. Physics 43 (1981), 357–372.
P. Roe, Discontinuous solutions to hyperbolic systems under operator splitting. Manuscript.
J. Smoller, Shockwaves and reaction-diffusion equations. New York Heidelberg Berlin.
G.A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J.of Comp. Physics 27 (1978), 1–31.
P. Woodward, P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks. J.Comp.Phys.54 (1984), 115–173.
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Kröner, D. (1989). Numerical schemes for the Euler equations in two space dimensions without dimensional splitting. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_35
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DOI: https://doi.org/10.1007/978-3-322-87869-4_35
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-08098-3
Online ISBN: 978-3-322-87869-4
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