Subgrid Modeling for Convection-Diffusion-Reaction in Two Space Dimensions Using a Haar Multiresolution Analysis.

In this paper we study a subgrid model based on extrapolation of a modeling residual, in the case of a linear convection-diffusion-reaction problem Lu=f in two dimensions. The solution u to the exact problem satisfies an equation L[sub h]u=[f][sup h]+F[sub h](u), where L[sub h] is the operator used in the computation on the finest computational scale h, [f][sup h] is the approximation of f on the scale h, and F[sub h](u) is a modeling residual, which needs to be modeled. The subgrid modeling problem is to compute approximations of F[sub h](u) without using finer scales than h. In this study we model F[sub h](u) by extrapolation from coarser scales than h, where F[sub h](u) is directly computed with the finest scale h as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a mesh of size less than h/4. [ABSTRACT FROM AUTHOR]