Output-based error estimation and grid adaptation

A mesh-adaptation criterion using output-based error estimation is developed to improve the accuracy of the output and the efficiency of computations. At first, the procedure of output-based error estimation and correction are described. Primal residual error and prescribed functional are related to each other by the adjoint method. The discrete adjoint solution is a weighting function, which weights the primal residual error. The error estimation and correction needn′t to compute the flow and adjoint solution on the fine mesh, which will be obtained by prolongation operation. Then, a strategy for grid adaptation is developed to reduce the remaining error after the functional correction and improve the accuracy of computations. Furthermore, the mesh adaptation method is extended to multi-object problems. The adaptation parameter is the remaining error, which contains both primal residual error and adjoint residual error. The governing equations are two-dimensional Euler equations. They are solved by using finite volume approximation and five-step Runge-Kutta temporal discretization. The adjoint is a discrete equation and its solution procedure is similar to that of governing equations. Finally, the strategy is applied to the simulation of inviscid compressible flows around the NACA0012 airfoil. Numerical experiments have successfully captured the features which are associated with the prescribed functional, produced integral outputs with desired accuracy, and finally validated the method developed in this article.