基于格点的非结构网格时域有限体积算法及其应用

Cell-vertex finite-volume time-domain algorithm on unstructured grid and its applications

为了避免传统算法电磁场基于对偶网格交错采样的做法,发展了一种电磁场基于单一非结构网格格点的时域有限体积算法。该算法借鉴了计算流体力学的做法,结合求解麦克斯韦方程,空间离散采用Steger-Warming通量分裂,时间离散则按照四步Runge-Kutta格式推进求解。通量运算涉及的控制体表面物理量的面值采用函数逼近重构确定。文中给出了基于格点的面值函数逼近重构的具体实施方法。算例表明:面值重构改通常的线性函数逼近为二次函数逼近可提高计算精度;由于算法是基于非结构网格的格点发展的,适合处理多体及多部件干扰等复杂情形。

In order to improve the traditional cell-vertex based methods, a cell-vertex finite-volume time-domain algorithm based on an unstructured grid is developed for solving the time-dependent Maxwell’s equations,which results in that all physical quantities at each time step can be updated at the vertices of the same mesh cell without using auxiliary mesh like traditional methods. Referring to the approaches used in computational fluid dynamics, Steger-Warming flux-vector splitting is introduced in spatial discretization, and an explicit four-stage Runge-Kutta scheme is employed in time-marching. Physical quantities on the surface of control volumes related to the flux computation are determined by a function reconstruction,which is described in details in this paper. Numerical results show that the accuracy of physical quantities used for the flux calculation on the surface of each control volume is improved by using the quadratic function reconstruction instead of the traditional linear function reconstruction. Numerical examples also show that the presented method has the ability to accommodate complex geometries with multi-element or multi-component due to the use of cell vertices of the unstructured grid.