论文信息 - Extrapolation methods for hyperbolic systems with relaxation

Extrapolation methods for hyperbolic systems with relaxation

Abstract A splitting scheme is used for numerical solution of hyperbolic systems with a stiff relaxation. High-order flux in the convection step guarantees a good spatial accuracy. The relaxation term is treated implicity. Extrapolation is used to combine the steps, obtaining high accuracy in time. A third-order scheme both in space and in time is presented and applied to the Broadwell model of gas dynamics.

[1] Tai-Ping Liu. Hyperbolic conservation laws with relaxation , 1987 .

[2] Richard B. Pember. Numerical Methods for Hyperbolic Conservation Laws With Stiff Relaxation I. Spurious Solutions , 1993, SIAM J. Appl. Math..

[3] S. Osher,et al. Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[4] G. Marchuk,et al. Difference Methods and Their Extrapolations , 1983 .

[5] Claude Brezinski,et al. Extrapolation methods - theory and practice , 1993, Studies in computational mathematics.

[6] Richard B. Pember. Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation II. Higher-Order Godunov Methods , 1993, SIAM J. Sci. Comput..

[7] G. Whitham,et al. Linear and Nonlinear Waves , 1976 .

[8] Giovanni Russo,et al. Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation , 1997 .

[9] L. Ahlfors. Complex Analysis , 1979 .

[10] R. LeVeque. Numerical methods for conservation laws , 1990 .

[11] J. Broadwell,et al. Shock Structure in a Simple Discrete Velocity Gas , 1964 .

[12] William B. Gragg,et al. On Extrapolation Algorithms for Ordinary Initial Value Problems , 1965 .