Mathematical Models and Methods in Applied Sciences · 2007 · 139 citations · 35 references
Natural SciencesComputational EngineeringComputational Fluid DynamicsFluid DynamicsHydrologic ModelingFlow ModelingNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsBalanced Numerical ModelsComputational Fluid Dynamics For Shallow WaterShallow Water EquationsShallow-water HydrodynamicsWell-balanced Schemes
The goal of this paper is to generalize the hydrostatic reconstruction technique introduced in Ref. 2 for the shallow water system to more general hyperbolic systems with source term. The key idea is to interpret the numerical scheme obtained with this technique as a path-conservative method, as defined in Ref. 35. This generalization allows us, on the one hand, to construct well-balanced numerical schemes for new problems, as the two-layer shallow water system. On the other hand, we construct numerical schemes for the shallow water system with better well-balanced properties. In particular we obtain a Roe method which solves exactly every stationary solution, and not only those corresponding to water at rest.
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