Third order nonoscillatory central scheme for hyperbolic conservation laws |
| |
Authors: | Xu-Dong Liu Eitan Tadmor |
| |
Institution: | (1) Department of Mathematics, UCSB, Santa Barbara, CA 93106, USA; e-mail: xliu@math.ucsb.edu , US;(2) School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel , IL;(3) Department of Mathematics, UCLA, Los Angeles CA 90095, USA; e-mail: tadmor@math.ucla.edu , US |
| |
Abstract: | Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented.
Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given
cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines
of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent),
in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann
solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution
content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected
third-order resolution.
Received April 10, 1996 / Revised version received January 20, 1997 |
| |
Keywords: | Mathematics Subject Classification (1991):65M10 65M05 |
本文献已被 SpringerLink 等数据库收录! |
|