Performance Comparison of the Three Numerical Methods to Discretize the Local Inertial Equation for Stable Shallow Water Computation
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.
KeywordsLocal inertial equation Finite difference scheme Friction slope term Tonle Sap Lake
This research was funded by SATREPS project “Establishment of Environmental Conservation Platform of Tonle Sap Lake” and JSPS research grant No. 17K15345.
- 2.Bates, P.D., Horritt, M.S., Fewtrell, T.J.: A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. J. Hydrol. 387(1–2), 33–45 (2012)Google Scholar
- 6.Yoshioka, H., Tanaka, T.: On mathematics of the 2-D local inertial model for flood simulation. In: Proceedings of the 2nd International Symposium on Conservation and Management of Tropical Lakes, Siem Reap, Cambodia, 24–26 August 2017, pp. 30–36 (2017)Google Scholar
- 10.Godunov, S.K.: A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations. Math. Sbornik 47, 271–306 (1969)Google Scholar
- 11.Tanaka, T., Yoshioka, H.: Applicability of the 2-D local inertial equations to long-term hydrodynamic simulation of the Tonle Sap Lake. In: Proceedings of the 2nd International Symposium on Conservation and Management of Tropical Lakes, Siem Reap, Cambodia, 24–26 August 2017, pp. 23–29 (2017)Google Scholar