Stabilized finite element approximation of transient incompressible flows using orthogonal subscales

摘要

In this paper we present a stabilized finite element method to solve the transient navier-Stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales. The latter are approximately accounted for, so as to end up with a stable finite element problem which, in particular, allows to deal with convection-dominated flows and the use of equal velocity-pressure interpolations. Three main issues are addressed. The first is a method to estimate the behavior of the stabilization parameters based on a Fourier analysis of the problem for the subscales.