一种基于Gordon-Hall方法的DGTD高阶网格生成技术

A DGTD High-Order Hexahedrons Generation Technology Based on Gordon-Hall Method

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 Hexahedron Discontinuous Galerkin Time Domain algorithm requires the computational domain divided into a set of nonoverlapping curved hexahedral subdomains, each subdomain＇s Jacobian matrix must be obtained by map it in- to a standard cube and get its mapping function. However, general commercial software can only divided computational do- main into straight or low order hexahedral meshes, these meshes poorly conform to the object＇s boundary and bring in errors in DGTD boundary condition. This article proposed the technique of arbitrary order curved hexahedral meshes combining with Gordon-Hall method, this kind of meshes conforms with the object＇s boundary more accurately, and reduces the mapping function deviation obviously. Numerical results verified the technique of generating high order curved hexahedral meshes can improve the accuracy of the DGTD algorithm without increase computing resources significantly.