Multiscale Dynamic Diffusion Method to Solve Advection-Diffusion-Reaction Problems
Andrea Valli1; Lucia Catabriga1; Isaac Santos2; Regina Almeida3; Alvaro Coutinho4
1 DI/UFES; 2 UFES; 3 LNCC; 4 COPPE/UFRJ
doi:10.20906/CPS/CILAMCE2015-0251
Resumo
In this work we evaluate different characteristic subgrid parameters, such as the subgrid velocity field and the length scale at which the subgrid inertial effects take place, for a finite element formulation for advection-diffusion-reaction problems using a continuous two-scale method denominated Dynamic Diffusion method (DD). In order to reduce the computational cost typical of two-scale methods, the subgrid scale space is defined using bubble functions whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. This method leads to a non-linear scheme which is solved by an iteration-lagging procedure that utilizes the bubble-enriched Galerkin solution as the correspondent approximation of the order zero. Here we also evaluate different indicators to represent the amount of artificial diffusivity that should be added by the numerical model, such as the size of the gradient of either the resolved scale solution or the subscale solution at each element. Numerical experiments were conducted to illustrate the behavior of the DD formulation for the different parameters applied to advection-diffusion-reaction equations. Performance and accuracy comparisons are based on benchmark 2D problems.
Palavras-chave: Multiscale Schemes; Dynamic Diffusion Method; Advection-Diffusion-Reaction Problems; Characteristic Subgrid Parameters