二维浅水方程的高阶松弛格式求解

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。

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

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 fifthorder 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.