Central schemes and contact discontinuities
Department of Mathematics, University of Michigan,
Ann Arbor, MI 48109-1109, USA. (firstname.lastname@example.org)
2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA. (email@example.com)
Revised: 2 October 2000
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.
Mathematics Subject Classification: 65M10 / 65M05
Key words: Euler equations of gas dynamics / partial characteristic decomposition / fully-discrete and semi-discrete central schemes.
© EDP Sciences, SMAI, 2000