求解浅水方程的五阶松弛格式(英文)  

A Fifth-order Relaxation Scheme for the Shallow Water Equations

作　　者：陈建忠[1] 史忠科[1] 胡彦梅[2] 

机构地区：[1]西北工业大学自动化学院,西安710072 [2]长安大学理学院,西安710064

出　　处：《工程数学学报》2010年第1期173-178,共6页Chinese Journal of Engineering Mathematics

基　　金：The Aoxiang Project of NPU;the Scientific and Technological Innovation Foundation of NPU(2007KJ01011)

摘　　要：对浅水方程,提出了一种具有五阶精度的松弛格式。该格式以五阶WENO重构和隐式Runge-Kutta方法为基础。格式保持了松弛格式简单的优点,即不用求解Riemann问题和计算通量函数的雅可比矩阵。应用该方法对一维平底和非平底溃坝问题进行了数值模拟,结果表明方法健全、有效。对摩阻源项也进行了讨论。A fifth-order relaxation scheme for the shallow water equations is presented in this paper. The scheme is based upon the fifth-order weighted essentially nonoscillatory （WENO） reconstruction and the implicit-explicit Runge-Kutta scheme. The resulting scheme does not require Riemann solvers and the computation of Jacobians, so it has the advantages of relaxation schemes. The resulting method is applied to simulate the one-dimensional dam- break problems on fiat and non-fiat topography. The results demonstrate the robustness and effectiveness of the present method. The effect of bottom friction is also discussed.

关 键 词：浅水方程 松弛格式 WENO重构 

分 类 号：O241.82[理学—计算数学]