A stabilized finite element approach for advective-diffusive transport problems

Abstract

[Abstract] As it is well-know, the numerical simulation in fluid mechanics is quite difficult specially when the velocity of the fluid is important. These problems are reflected in the apparearance of numerical oscillations when Finite Element approaches with Galerkin weighting are used. In last years, some alternative formulations have been proposed in order to overcome these problems: Streamline Upwind Petrov Galerkin Methods, Space-time Galerkin Least Squares Methods, Subgrid Scale Methods, Characteristic Galerkin Method, etc. In this paper, we focuse our attention in the advective-diffusive transport differential equation, and its application to engineering problems. Thus, we present a brief review of the causes of appaerance of these numerical oscillations and a short revision of the numerical schemes proposed for the stabilization of advective-dominant problems. Then, a numerical formulation based on a Petrov Galerkin scheme and a procedure to obtain stabilization parameters for 1D, 2D and 3D problems are proposed. Finally, we present different numerical test problems, and we show the feasibility of this formulation with its application to an engineering problem: the evolution of a water pollutant spilt in a harbour area.