Output-based Error Estimation And Mesh Adaptation

In this thesis，a mesh-adaptation criterion using output-based error estimation isdeveloped to improve the accuracy of the output. At first, output-based error estimation andcorrection procedure are described. The original residual error and prescribed functional areconnected by using the adjoint method. The discrete adjoint solution is a weighting function,which weights the original residual error. During the procedure of error estimation andcorrection, the variables on the coarse mesh are mapped to the fine mesh. No calculation ofvariables on fine mesh is required. Thereafter, based on the correction and remaining error, astrategy of mesh adaptation is developed to reduce the remaining error after functionalcorrection and to improve the accuracy of computation. Furthermore, the mesh adaptationmethod is extended to handle the multi–object problems. The adaptation parameter is theremaining error, which contains both original residual error and adjoint residual error, and itschoice will be more stable and effective. The governing equations for flow field aretwo-dimensional Euler equations, which are solved by finite volume approximation andfive-step Runge-Kuta temporal discretization. The adjoint equation is in discrete form and itssolution procedure is similar to that of governing equations. Finally, the strategy is applied tothe simulation of inviscid compressible flows around the NACA0012airfoil. Numericalexperiments have successfully captured the features which are associated with the prescribedfunctional, produced intergral outputs with desired accuracy, and finally validated theproposed scheme.