Implicit finite volume simulation of 2D shallow water flows in flexible meshes

- We use a 2D implicit surface flow model based on shallow water equations.
- A robust wet/dry treatment is implemented.
- The scheme is validated by means of exact solutions and experimental data.
- CFL numbers up to 300 are reached.
- The efficiency of the implicit scheme is explored.

In this work, an implicit method for solving 2D hyperbolic systems of equations is presented, focusing on the application to the 2D shallow water equations. It is based on the first order Roe's scheme, in the framework of finite volume methods. A conservative linearization is done for the flux terms, leading to a non-structured matrix for unstructured meshes thus requiring iterative methods for solving the system. The validation is done by comparing numerical and exact solutions in both unsteady and steady cases. In order to test the applicability of the implicit scheme to real world situations, a laboratory scale tsunami simulation is carried out and compared to the experimental data. The implicit schemes have the advantage of the unconditional stability, but a quality loss in the transient solution can appear for high CFL numbers. The properties of the scheme are well suited for the simulation of unsteady shallow water flows over irregular topography using all kind of meshes.