High resolution methods for multidimensional advection-diffusion problems in free-surface hydrodynamics

In this paper the numerical solution of advection-diffusion problems in free-surface hydrodynamic is analyzed. A new finite volume scheme for unstructured grid is derived. It is shown how both, mass conservation and maximum principle can be assured by the present method. The issue of numerical accuracy is also addressed in two and three-dimensional problems. Suggestions for grid generation are also implied.