An adjoint-truncation error based approach for goal-oriented mesh adaptation

We present the development and validation of an output-based mesh adaptation approach which combines the adjoint methodology with the τ-estimation technique for truncation error estimation. The approach relies on the use of an auxiliary coarse mesh to estimate the functional error and drive the mesh adaptation. The functional is estimated with an error representation formula given by the inner product of the adjoint solution and the discrete residual of the exact solution, which is approximated by the τ-estimation method. This method avoids the use of an embedded fine grid which is the common approach in the adjoint-based adaptation methods. Furthermore, it also allows to reduce the computational time overhead per adaptation step because the adjoint solution is obtained on a coarser mesh level. The effectiveness of the method is demonstrated in the framework of unstructured-mesh finite volume discretization for two- and three-dimensional Euler flows and comparisons against several mesh adaptation approaches are shown.