A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations

被引：180

作者：

Kurganov, A ^{[1
]}

Levy, D

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[3] Univ Calif Berkeley, Lawrence Berkeley Lab, Berkeley, CA 94720 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2000年 / 22卷 / 04期

关键词：

hyperbolic systems; convection-diffusion equations; central difference schemes; high-order accuracy; nonoscillatory schemes; weighted essentially nonoscillatory reconstruction;

D O I：

10.1137/S1064827599360236

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a new third-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semidiscrete method in [A. Kurgonov and E. Tadmor, J. Comput Phys., 160 (2000) pp. 241-282]. The method is derived independently of the specfic piecewise polynomial reconstruction which is based on the previously computed cell-averages. We demonstrate our results by focusing on the new third-order central weighted essentially nonoscillatory (CWENO) reconstruction presented in [D. Levy, G. Puppo, and G. Russo, SIAM J. Sci. Comput., 21 (1999), pp. 294-322]. The numerical results we present show the desired accuracy, high resolution, and robustness of our method.

引用

页码：1461 / 1488

页数：28

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