Efficient A Posteriori Error Estimation for Finite Volume Methods

The propagation of error in numerical solutions of the compressible Navier-Stokes equations is examined using linearized, and adjoint linearized versions of the discrete flow solver. With the forward linearization it is possible, given a measure of the local residual error in the field, to obtain estimates of global solution error. This allows for example the computation of error estimates on pressure distributions. With the backward or adjoint linearization it is possible, for any given scalar output quantity, to identify those regions of the field which contribute the most to the error in that quantity. This information may be used to refine the mesh in a way that minimizes error in this output functional. Both approaches are be used, not only to provide accurate error estimates, but also to correct the output. In the following we concentrate on the solution error due to explicitly added artificial dissipation in the spatial discretization. By comparing with the true solution error obtained using mesh refinement studies, it is seen that this can be applied as an effective total error indicator for mesh adaptation.