用半离散中心迎风格式计算一维浅水方程

Numerical solution of one-dimensional shallow water equations by semi-discrete central-upwind scheme

将半离散中心迎风数值通量和三阶WENO重构结合起来,由此得到了一种求解一维浅水方程的高分辨率数值方法.对底坡项的离散保证了计算方法的和谐性,离散摩阻项的方法简单有效.时间的离散采用保持强稳定性质的Runge-Kutta方法.应用文中方法对几个典型算例进行检验计算,结果表明本文方法健全,而且对激波具有较高的分辨率.

A high-resolution method for solving one-dimensional shallow water equations is presented by combing the semi-discrete central-upwind numerical flux with the third-order weighted essentially non-oscillatory （WENO） reconstruction. The discretization of bottom topography assures well-balanced approximation and the discretization of friction slop is simple and effective. The third-order strong stability preserving Runge-Kutta method is used for time discretization. Validity of several typical samples show that this method is effective and has high precision for shock waves.