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基于六面体的时域间断伽略金方法(Hex-DGTD)要求将计算域划分为一系列互不重叠的六面体子域,通过求解每个子域到标准立方体的映射函数得到各子域内的Jacobian矩阵。然而一般商业软件仅能够将计算域划分为线性或者较低阶数的六面体网格,这种与目标表面近似度较低的六面体将导致DGTD算法中边界条件设置存在误差。文中结合Gordon-Hall方法提出了任意高阶数的网格生成技术,能够更为精确地模拟出目标表面,大幅减小了求解六面体子域映射函数的误差。最后通过算例验证了这种高阶六面体网格生成技术能够在不明显增加计算资源的前提下,较大程度地提升DGTD算法的求解准确度。
The Hex-DGTD method requires that the computational domain be divided into a series of non-overlapping hexahedral sub-domains, and the Jacobian matrix in each sub-domain is obtained by solving the mapping function of each sub-domain to a standard cube. However, commercial software can only divide the computational domain into linear or lower-order hexahedral meshes. The hexahedron with a low degree of similarity to the target surface will lead to the errors of the boundary conditions in the DGTD algorithm. In this paper, an arbitrary high-order mesh generation technique is proposed based on the Gordon-Hall method, which can simulate the target surface more accurately and greatly reduce the error of solving the mapping function of the hexahedral sub-fields. Finally, an example is given to verify that this high-order hexahedral mesh generation technology can greatly improve the accuracy of DGTD algorithm without significantly increasing the computational resources.