Numerical Solutions of One-Dimensional Shallow Water Equations

This paper investigates the application of finite difference methods to solve the Shallow Water Equations (SWE's), in the context of mesh refinement through the introduction of an error tolerance. The problem is tackled by linearisation of the nonlinear differential equations through the discretization process. Once the set of equations have been linearised discretely, they are then solved. The solution set is then used to derive error values at nodes in space for individual time points. This error is then tested against a predefined tolerance; pending test results, the mesh is refined.