Performance Comparison of the Three Numerical Methods to Discretize the Local Inertial Equation for Stable Shallow Water Computation

Abstract

The local inertial equation (LIE) is a simple shallow water model for simulating surface water dynamics. Recently, the model has been widely applied to flood simulation worldwide. Keys in numerical implementation of the LIE are the staggered spatio-temporal discretization and the stable treatment of the friction slope terms. The latter is critical for stable and efficient computation. Currently, several discretization methods (semi-implicit, fully-implicit, and exponential methods) for the friction slope terms with comparable computational efficiency are available. However, their performance evaluation has been carried out only independently. We thus compare the performance of the three methods through their application to test and realistic cases. In this paper, firstly, theoretical linear stability analysis results are reviewed, indicating the highest stability of the implicit method. It is also consistent in a certain sense. Application of these methods to a 1-D test case with an advancing wet and dry interface implies that all the methods work well where the fully-implicit method has the least error. Their application to 2-D flood simulation in Tonle Sap Lake and its floodplains in South-East Asia demonstrates that the exponential method gives slightly more oscillatory results than the others. Dependence of the simulated surface water dynamics on the spatial resolution is investigated as well to give a criterion of the resolution for numerical simulation with satisfactory accuracy.