二维浅水方程的高阶松弛格式求解  

Numerical solution of the two-dimensional shallow water equations by high order relaxation scheme

作　　者：陈建忠[1] 史忠科[2] 胡彦梅[2] 

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

出　　处：《水动力学研究与进展（A辑）》2007年第3期305-310,共6页Chinese Journal of Hydrodynamics

摘　　要：利用松弛方法,将二维浅水方程转化为松弛方程组,并用逐维五阶WENO重构和显隐式Runge-Kutta方法对松弛方程组的空间和时间方向进行离散,建立了求解二维浅水方程的五阶松弛格式。WENO重构方法的引入既提高了格式的精度,又可保证格式是无振荡的。应用该格式对圆柱溃坝等问题进行了数值模拟,计算结果与用其它方法所得结果吻合,表明了方法的有效性。A fifth-order relaxation scheme for the two-dimensional shallow water equations is proposed in this paper. The scheme is based on replacing two-dimensional shallow water equations by the relaxation system. The spatial discretization and time integration of the relaxation system are implemented by a fifth-order weighted essentially non-oscillatory（WENO） reconstruction and the implicit-explicit Runge-Kutta method, respectively. The WENO reconstruction is chosen to improve the accuracy and guarantee the non-oscillatory behavior of the present scheme. The resulting method is applied to simulating several tests, in particular, circular dam-break problem. The results show in good agreement with numerical results obtained by other methods. The simulated results also demonstrate that the presented method is stable and efficient.

关 键 词：二维浅水方程 松弛格式 WENO重构 逐维方法 

分 类 号：TV131.4[水利工程—水力学及河流动力学]