Volume 34, Number 6, November/December 2000
|Page(s)||1259 - 1275|
|Published online||15 April 2002|
Central schemes and contact discontinuities
Department of Mathematics, University of Michigan,
Ann Arbor, MI 48109-1109, USA. (email@example.com)
2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA. (firstname.lastname@example.org)
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.