基于伴随方法的网格自适应DG方法

发布时间：2018-12-07 16:33

【摘要】：发展了一套基于伴随方法的Euler方程自适应网格DG求解方法,采用当地网格上的输出变量的误差估计作为离散误差指示器驱动网格自适应.在离散误差指示器的构造中,采用GMRES方法求解伴随方程获得伴随变量,将p阶流场变量和伴随变量映射到p+1阶函数空间,并进行有限次块对角Jacobi迭代得到近似p+1阶细网格解.壁面边界通量及输出变量计算仅依赖边界外侧值以保证伴随相容性.首先采用NACA0012翼型不同精度的阻力系数结果验证了误差估计的可靠性,然后对NACA0012翼型亚声速、跨声速流场和圆柱6马赫高超声速绕流进行了自适应加密计算研究.研究结果表明,基于伴随方法的网格自适应可有效提高阻力系数等输出变量的模拟准确性,在亚声速NACA0012翼型计算中使用约17%的全局加密自由度获得了与全局加密精度相当的阻力系数.
[Abstract]:A set of adaptive mesh DG solutions for Euler equation based on adjoint method is developed. The error estimation of the output variables on the local grid is used as the discrete error indicator to drive the mesh adaptation. In the construction of discrete error indicator, the adjoint variable is obtained by solving adjoint equation by GMRES method, and the p order flow field variable and adjoint variable are mapped to the function space of p 1 order. The finite block diagonal Jacobi iteration is used to obtain the approximate p1 order fine grid solution. The calculation of wall boundary flux and output variables only depends on the lateral boundary value to ensure adjoint compatibility. The reliability of the error estimation is verified by the results of the drag coefficients of the NACA0012 airfoil with different accuracy. Then, the adaptive encryption calculation of the subsonic velocity, transonic flow field and the hypersonic flow around the cylinder 6 Mach is carried out for the NACA0012 airfoil. The results show that the mesh adaptation based on adjoint method can effectively improve the simulation accuracy of output variables such as drag coefficient. In the calculation of subsonic NACA0012 airfoil, about 17% of the degree of freedom of global encryption is used to obtain the resistance coefficient equivalent to the precision of global encryption.
【作者单位】：中国航天空气动力技术研究院;
【分类号】：O241.8

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