中文摘要：

发展了一种基于目标函数误差估算的网格自适应准则,进而通过网格自适应处理提高目标函数计算的效率和准确性。首先描述了目标函数的误差估算及修正的方法,该方法通过伴随方程将原方程的残值误差与目标函数联系起来。然后,基于误差估算建立网格自适应准则,以减少目标函数修正后的剩余误差,提高目标函数计算结果的准确性,并将方法进一步发展至多目标问题。最后将该准则应用于Euler方程控制的NACA0012翼型无粘可压流动的网格自适应模拟。数值计算成功地捕获了与升力、阻力和力矩等目标函数相关的特征流动区域,计算出符合指定精度要求的目标函数值,验证了本文所发展的方法。

英文摘要：

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 esti-mation 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 resid-ual 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.Fur-thermore,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 e-quations are two-dimensional Euler equations.They are solved by using finite volume approximation and five-step Rungge-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 com-pressible 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 fi-nally validated the method developed in this article.