Artificial Diffusion Methods in Convection Dominated Flows

摘要

A stationary scalar linear convection-diffusion equation is considered. For theone dimensional equation a standard Galerkin formulation, which serves at the same time as an introduction to the Finite Element Method (FEM) is deduced. The eigenvalues of the resulting stiffness matrices are examined. For the two dimensional problem, the oblique shock, the same equation is formulated with suppression of the 'crosswind diffusion'. The diffusion resulting from specific time integration techniques is examined, using space-time FEM and discontinuous Galerkin method. Navier-Stokes equations are derived and results of an implementation of the Streamline Upwind Petrov Galerkin (SUPG) method for the flow over a step and the backward facing step are given. The Galerkin/least squares method is discussed.