Mathematical Development and Verification of a Finite Volume Model for Morphodynamic Flow Applications (Advances in Applied Mathematics and Mechanics, 2011)
The accuracy and efficiency of a class of finite volume methods are investigated for numerical solution of morphodynamic problems in one space dimension. The governingequations consist of two components, namely a hydraulic part described by the shallowwater equations and a sediment part described by the Exner equation. Based on differentformulations of the morphodynamic equations, we propose a family of three finite volumemethods. The numerical fluxes are reconstructed using a modified Roe's scheme thatincorporates, in its reconstruction, the sign of the Jacobian matrix in the morphodynamicsystem. A well-balanced discretization is used for the treatment of the source terms.The method is well-balanced, non-oscillatory and suitable for both slow and rapidinteractions between hydraulic flow and sediment transport. The obtained results forseveral morphodynamic problems are considered to be representative, and might be helpfulfor a fair rating of finite volume solution schemes, particularly in long time computations.