Grid Adaptation Using Adjoint-Based Error Minimization

We have recently introduced 1 a new adjoint-based grid adaptation methodology that directly solves an error minimization problem. The methodology has been previously applied to the problems for which the true error is available. In this paper, the methodology is extended to general formulations in which the true error is not employed. Two sets of adjoint variables are introduced. The rst set is used to estimate the error in a functional output of interest (e.g., lift, drag, thrust, etc.). The output error is estimated as an inner product of the residual and the adjoint variables associated with the functional output. The second set is used to compute sensitivity of the error estimate with respect to the mesh coordinates. For the practical error functional considered in this paper, only one set of adjoint equations needs to be solved to nd the both sets of adjoint variables. The methodology of grid adaptation combines grid renemen t with grid redistribution. One advantage of this automated grid adaptation methodology is that the number of adjoint solutions used at each optimization iteration is independent of the number of grid nodes. Another advantage is that grid redistribution provides a rigorous metric-free mechanism to relate the estimated error in the functional output to the size, shape, and orientation of grid elements. Thus this approach is very well suited for anisotropic grid adaptation. In this paper, the adjoint-based grid adaptation strategy is tested on several problems governed by the 2-D steady Poisson and Euler equations.