Numerical Tracking of Shallow Water Waves by the Unstructured Finite Volume WAF Approximation

Abstract

The depth averaged shallow water equations (s.w.e.) are useful and reliable for dam break flow and flood modeling. For their approximation, the finite volume method (FVM) in conjunction with Riemann solvers permits shock capturing. This work provides an overview of the FV weighted average flux (WAF) method applied to s.w.e., and its implementation on unstructured triangular or quadrilateral meshes. The inviscid fluxes are given by the HLLC solver, and stabilization is ensured by the proper WAF limiters inherited from the total variation diminishing (T.V.D.) theory. Additional numerical improvements are incorporated to the model, such as enhancing the calculation of bed slopes, using an optional semi-implicit discretization of the friction source term, and affecting a depth tolerance to dry areas. The model performance is displayed through the simulation of well known synthetic and experimental examples including CADAM test 1 and test 2, which all show that the predictions are accurate and that the triangular mesh seems more efficient than quadrilateral. The applicability to real cases is assessed by simulating the flooding flow in a breakwater on “rivière des Prairies” having an irregular bathymetry.