用于起伏地表条件下地球物理场数值模拟的正交曲网格生成技术

Orthogonal curvilinear grid generation technique used for numeric simulation of geophysical fields in undulating surface condition

起伏地表条件下地球物理场数值模拟所面临的主要困难在于如何求解自由边界(地—空界面)上的边界条件。如今虽有多种解决途径,如映射法、插值法和不规则网格法,但均存在一些问题,本文针对上述方法的问题提出了一种新的解决途径。首先引入了在计算流体力学中发展起来的贴体正交网格技术,通过对弹性波场和直流电场在地—空界面上所应满足的微分方程(边界条件)的分析,得到了正交曲网格优于非正交曲网格的结论;然后利用基于泊松方程的网格生成方法,采用Hilgenstock法控制源项,并结合代数辅助方法生成了正交贴体曲网格。结果表明,本文所用的网格生成方法适用于解决起伏地表条件下地球物理场的数值模拟问题。

The difficulty faced in numeric simulation of geophysical fields under the undulating surface condition lies how to solve the boundary condition in free-boundary (earth-to-space interface). Although there have been many ways until now,for example,mapping method,interpolation method and non-orthogonal grid method etc,all of them have some problems. In view of abovementioned difficulties,the paper presented a new solving way. First,introducing the orthogonal body-fitted grid technique developing in computation of fluid mechanics,the conclusion that the orthogonal curvilinear grid is superior to non-orthogonal curvilinear grid was gained by analyzing the differential equation (boundary condition) that should be met by elastic wavefield and DC electrical field in earth-to-space interface; then,using grid generation method based on Poisson equation and adopting Hilgenstock method to control source term,the orthogonal body-fitted curvilinear grid was generated in combination with algebraic auxiliary method. The results showed that the grid generating method presented in the paper is suitable to solve the numeric simulation issue of geophysical fields in undulating surface condition.