On dynamic computational subgrid modeling

Abstract

In this paper we study a subgrid model based on extrapolation of a corrective force, in the case of a linear convection-diffusion problem in one dimension. The running average of the exact solution on the finest computational scale satisfies an equation , where is the operator used in the computation on the scale , is the approximation of on the scale , and acts as a corrective force, which needs to be modeled. The subgrid modeling problem is to compute approximations of without using finer scales than . In this study we model by extrapolation from coarser scales than where the corrective force is directly computed with the finest scale as reference. We show in experiments that a corrected solution with subgrid model on scale corresponds to a non-corrected solution on less than .