Dynamic Diffusion Formulation for Advection Dominated Transport Problems

Abstract

Two discontinuous dynamic diffusion formulations for the numerical solution of advectiondiffusion equations are proposed in this work. The first one reformulates, using broken spaces, the Consistent Approximate Upwind Petrov-Galerkin (CAU) finite element model. The second one considers a two-scale framework and introduces an artificial diffusion to DG formulation that acts isotropically in both scales. The amount of artificial diffusion is dynamically determined by the resolved scale solution at an element level, yielding a self adaptive and parameter-free method. This formulation takes into account the effective flux through inter-element edges to keep the consistency property. Numerical experiments are conducted, which cover a variety of problem parameter ranges, in order to show the behavior of the proposed methods in comparison with some discontinuous Galerkin methods.