2维和2.5维起伏地表直流电法有限差分数值模拟

起伏地表直流电场数值模拟现多采用有限元法,主要是因为其有灵活的处理曲边界的能力,然而有限元法比有限差分法要复杂,如果让有限差分法也同样具有较好的处理曲边界的能力,那数值模拟将变得更为简单.本文通过在非正则内点处采用不等距差分,在起伏地表点处直接实现边界条件,克服转移法人为改变地表形状的弊端,使得基于笛卡尔网格的有限差分...

Finite-difference DC electrical field modeling on 2D and 2.5D undulate topography

Undulate surface DC field numerical simulation using finite element method is commonly used, mainly because of its flexible curved boundary treatment capacity. However, finite element is more complex than the finite difference. If we allow the finite difference to have also similar ability to deal with the curved boundary, that simulation will become easy. In this paper, non-equidistant difference is used at non-regular interior points and the boundary conditions are directly implemented to the undulate surface points, which overcomes the drawback of transfer method to change the shape of the surface, making finite-difference based on the Cartesian grid have a strong ability to deal with the boundary. Through the comparison of numerical and analytical solutions of the level surface in two-dimension and 2.5 dimension, as well as the two-dimensional numerical solution for undulate surface and the solution of conformal mapping theory, it is shown that the method is effective. Finally, we give some numerical examples.