A Posteriori Error Estimation for Subgrid Flamelet Models

Abstract

A dual-weighted residual error estimation strategy is applied to the modeling error associated with a class of subgrid scale models widely used in turbulent combustion. The approach is implemented and validated for an idealized test problem consisting of a system of multiscale advection-reaction-diffusion equations. The regime of interest corresponds to the limit of fast reaction. A fully resolved numerical simulation of the resulting very fine reaction scale would be excessively demanding, so typically a subgrid model is used instead to account for its impact at large scales. The class of subgrid models investigated here is based on the asymptotic flamelet approximation, which leads to the so-called flamelet libraries, i.e., precomputed tables expressing the reactive scalars in terms of the appropriate passive scalar. We show that a similar library can be constructed for the dual-based estimator. The performance of the estimation strategy is validated by comparison with exact results for steady and unsteady test cases. Asymptotic scalings are recovered, and new light is shed on some specific implementations of the flamelet models for unsteady test cases.