Comparison of two mathematical models for solving the dam break problem using the FEM method

This paper describes and compares two mathematical models for solving the dam break problem using the FEM. The first method solves the Navier–Stokes equations considering two immiscible and incompressible fluids, assigning the density and viscosity according to an indicator function whose zero level set determines the interface position. The second method is based on solving the Shallow Water equations using the well known Two-Step Taylor–Galerkin method. In this case, the problem becomes one of a drying and wetting one. This problem is simply handled by assigning null depth and velocity of the calculated dry nodes when performing the integrals over the elements in the mesh.The comparison of the results from the two methods for a number of test cases reveals the shortcomings of the Shallow Water approach. However, when considering the computational effort required by each method, the Shallow Water approach should be considered as a major candidate for computations involving large domains, leaving the Navier–Stokes approach for fine calculations where knowledge of the 3D structure of the flow is required.