Numerical Simulation of the Darcy’s Problem on Surfaces in R3
Monday 22nd July 2013
In the simulation of a flow in a porous medium, a key aspect is the treatment of fractures, local strong heterogeneities of the subsoil, characterized by a very small size in comparison with that of the whole basin. In order to solve this problem in literature was introduced a reduced model, which consists in considering the fracture as a n-1 dimensional surface immersed in a n-dimensional domain. In this work we consider the Darcy’s problem defined on a generic two-dimensional surface. We give an analysis of the properties of the numerical discretization of the problem, focusing on the relationships between the variables defined on the discrete surface and those defined on the real one, finally providing an estimate for the discretization error. We then implemented, within the finite element library LifeV, the C++ code for computing a numerical solution of the problem.