基于伴随方程的网格自适应及误差修正

Adjoint equations-based grid adaptation and error correction

基于流场方程的离散伴随优化理论和三维非结构网格,建立了网格自适应技术和目标函数误差修正方法。详细研究了用流动伴随变量进行目标函数的误差估计和修正技术,构造了适用于格心格式有限体积法的流场变量插值技术和网格单元剖分判据,初步实现了网格物面投影和空间单元优化,发展了适用于有限体积法的整套网格自适应方法。对NACA0012翼型和ONERA-M6机翼绕流进行了自适应数值模拟,并对升、阻力等目标函数进行了误差修正。数值结果表明,本文自适应方法能正确地捕捉到影响目标函数计算精度的敏感区域,网格自适应和误差修正两项技术显著提高了升、阻力等目标函数的计算精度。

Based on the discrete adjoint optimizing theory and three-dimensional unstructured grid,agrid adaptation technology and an error correction method for objective function are built.A method to predict and correct the error of objective function using adjoint equations is presented.Then,an interpolation technology which suits for centre-based finite volume method is proposed,some methods to divide tetrahedral grids,project surface grids and optimize spatial grids are discussed,and a complete grid adaptation system which suits for finite volume method is built.Finally,the grid adaptation method is applied to the simulation of inviscid flows around NACA0012 airfoil and ONERA-M6 wing,and the error of objective function,such as the coefficient of drag and lift,is corrected.Numerical results show that the sensitive grids for objective function are detected and refined by this grid adaptation method,and the accuracy of objective function is obviously improved after grid adaptation and error correction.