Finite Element Modeling of Free Surface Flow in Variable Porosity Media

The aim of the present work is to present an overview of some numerical procedures for the simulation of free surface ows within a porous structure. A particular algorithm developed by the authors for solving this type of problems is presented. A modi ed form of the classical Navier Stokes equations is proposed, with the principal aim of simulating in a uni ed way the seepage ow inside rock lllike porous material and the free surface ow in the clear uid region. The problem is solved using a semi-explicit stabilized fractional step algorithm where velocity is calculated using a 4th order Runge-Kutta scheme. The numerical formulation is developed in an Eulerian framework using a level set technique to track the evolution of the free surface. An edge-based data structure is employed to allow an easy OpenMP parallelization of the resulting nite element code. The numerical model is validated against laboratory experiments on small scale rock ll dams and is compared with other existing methods for solving similar problems.