Dimensional Splitting Well-Balanced Schemes on Cartesian Mesh for 2D Shallow Water Equations with Variable Topography

We present two types of simple algorithms for numerical approximations of the two-dimensional shallow water equations with variable topography by a dimensional splitting approach. The scheme of the first type has two steps and the the one of the second type has three steps of splitting dimensions in each iteration. In each step, the component computation incorporates a well-balanced method on Cartesian mesh in one-dimensional space. Tests show that these schemes provide us with a reasonable accuracy. Furthermore, we also establish the well-balanced property for both types of schemes.