A Posteriori Estimation of Error due to Dissipation in Finite Volume Schemes and Application to Mesh Adaptation

Abstract

A method is proposed to estimate a posteriori that part of the total discretization error which is attributable to the smoothing effect of added dissipation, for finite volume discretizations of the Euler equations. This is achieved by observing variation in a functional of the solution as the level of dissipation is varied, and it is deduced for certain test-cases that the dissipation alone accounts for the majority of the functional error. Based on this result an error estimator and mesh adaptation indicator is proposed for functionals, relying on the solution of an adjoint problem. The scheme is considerably implementationally simpler and computationally cheaper than other recently proposed a posteriori error estimators for finite volume schemes, but does not account for all sources of error. In mind of this, emphasis is placed on numerical evaluation of the performance of the indicator, and it is shown to be extremely effective in both estimating and reducing error for a range of 2d and 3d flows.