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Central schemes and contact discontinuities

Published online by Cambridge University Press:  15 April 2002

Alexander Kurganov  and
Guergana Petrova
Alexander Kurganov
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA. (kurganov@math.lsa.umich.edu)
Guergana Petrova
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA. (petrova@math.lsa.umich.edu)
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Abstract

We introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes, proposed in [A. Kurganov et al., submitted to SIAM J. Sci. Comput.], whose construction is based on the maximal one-sided local speeds of propagation. We also present a recipe, which helps to improve the resolution of contact waves. This is achieved by using the partial characteristic decomposition, suggested by Nessyahu and Tadmor [J. Comput. Phys.87 (1990) 408-463], which is efficiently applied in the context of the new schemes. The method is tested on the one-dimensional Euler equations, subject to different initial data, and the results are compared to the numerical solutions, computed by other second-order central schemes. The numerical experiments clearly illustrate the advantages of the proposed technique.

Keywords

Euler equations of gas dynamicspartial characteristic decompositionfully-discrete and semi-discrete central schemes.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 6 , November 2000 , pp. 1259 - 1275
Copyright
© EDP Sciences, SMAI, 2000

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