一维浅水方程的高精度GODUNOV格式

被引：17

作者：

耿艳芬

王志力

金生

机构：

[1] 大连理工大学土建学院海岸和近海工程国家重点实验室

来源：

水动力学研究与进展(A辑) | 2005年 / 04期

关键词：

一维浅水方程; HLLE黎曼解; 间断捕捉; 通量限制器;

D O I：

10.16076/j.cnki.cjhd.2005.04.016

中图分类号：

TV131.6 [水工试验];

学科分类号：

摘要：

以HLLE的近似Riemann解为基础,时间积分采用改进的二步RUNGE-KUTTA法,空间通过重构和通量限制获得时间和空间均为二阶精度的一维浅水方程的Godunov离散格式。此格式具有TVD的性质,保证了数值解收敛于弱解,在TVD意义下无假振,保持初值的单调性,解自动满足熵条件。通过实例比较了各种通量限制因子在求解方程中的优缺点,验证了此方法具有守恒性、鲁棒性、无虚假振荡并能高分辨率地捕捉间断等优点。

引用

页码：507 / 512

页数：6

共 10 条

[1]

Uniformly high order accurate non oscillatory scheme. HARTEN A,ENGQUIST B,OSHER S and CHAKRAVARTHY S R. Journal of Computational Physics . 1978

[2]

Upwind methods for hyperbolic conservation laws with source terms. BERMUDEZ A,VAZQUEZ ME. Computers and Fluids . 1994

[3]

Uniform high order spectral method for one and two dimensional Euler equations. CAI Wei,SHU Chi-wang. Journal of Computational Physics . 1993

[4]

On Godunov-type methods for gas dynamics. EINFELDT B. SIAM Journal on Numerical Analysis . 1988

[5]

A well behaved TVD limiter for high resolution calculations of unsteady flow. MOHIT A,PHILIP L R. Journal of Computational Physics . 1997

[6]

High order accurate difference solutions of fluid mechanics problems by a compact differening technique. RICHARD S HIRSH. Journal of Computational Physics . 1975

[7]

Dam break flow simulation: some results for one-dimensional models of real cases. NAVARRO P G,FRAS A,VILLANUEVA I. J Hydro . 1999

[8]

Improve application of the HLLE Rieman solver for the shallow water equation with source term. DELIS A I. Communications in Numerical Methods in Engineering . 2003

[9]

On the numerical dissipation of high resolution schemes for hyperbolic conservation laws. CLAUS DIETER MUNZ. Journal of Computational Physics . 1988

[10]

Balancing source terms and flux gradient in high-resolution Godunov method: the quasi steady wave propogation algorithm. LEVEQUE RJ. Journal of Computational Physics . 1998

← 1 →