半隐式的离散格式求解一维浅水流动

Semi-implicit discrete scheme for solving one-dimensional shallow water flow equation

为了对一维浅水流动问题进行精确的模拟,基于空间交错网格系统,建立了一维圣维南方程的半隐式数值离散格式,同时利用满足迎风特性的,加限制的通量修正格式对对流项进行处理,确保了交错网格系统下计算格式的守恒性.通过典型间断问题说明格式具备高精度捕捉间断的能力,而且避免了数值解在间断处产生非物理的数值振荡.

To accurately simulate the flow of one-dimensional shallow water,a semi-implicit scheme is proposed based on space staggered grid system.The flux limiter method is employed to control the accuracy of the proposed scheme to guarantee the conservation of the scheme.A few computational examples on classical test cases are given to illustrate the properties of the present method in terms of stability,accuracy and efficiency.