Performance of High-Resolution, Nonlevel Bed, Shallow-Water Models

Several techniques are investigated for extending Roeʹs finite volume method to second-order spatial and temporal accuracy in order to better simulate shallow water flow over nonlevel beds. Specifically, methods reported in the literature for limiting and reconstructing dependent variables, discretizing source terms, and time stepping are examined. Steady subcritical and supercritical flow as well as unsteady flow over nonlevel beds is simulated in order to evaluate each methodsʹ performance in terms of error and computational effort. There is not a single method which minimizes error and computational effort for all test cases. On the contrary, methods that perform best in one application may be suboptimal in another. A general purpose modeling approach that balances accuracy against computational effort is identified and recommended.