Computing stabilization parameters in numerical models for advective-diffusive transport problems

Abstract

[Abstract] Numerical modelling in Fluid Mechanics is particulary difficult in high-advective fluid problems. The Finite Element Method, which has been sucessfully applied to very challenging problems in Computational Mechanics, present some troubles in the resolution of high velocity fluid problems due to the appaerance of important oscillations of the sollution in specific parts of domain. In this paper, we consider the advective-diffuser trasport differential equation, which models a great number of problems in engineering. We briefly review the origin of the numerical oscillations and the alternative approaches proposed to overcome these phenomena, and we propose a procedure to obtain stabilization parameters in Petrov-Galerkin formulations from the eigenvalue analysis of the elemental matrices in the discretized problem. Finally, we present and discuss the result obtained for different tests problems.