Three dimensional simulation of GPR in tunnel hidden disease based on RSG algorithm

Abstract

The finite-difference method (FDM) algorithm with staggered grid greatly improved the computational efficiency of solving differential equations in two dimensional simulation of GPR, but the strict Courant-Friedrich-Levy (CFL) condition must be satisfied. In three dimensional simulation of GPR, a maximum time-step size will lead to a serious numerical dispersion, while a minimum time-step size will increase the computation time with higher cost. The rotated staggered grid (RSG) algorithm achieves a balance between computational efficiency and numerical stability in three dimensional simulations, as it solves the linear correlation of field value along the diagonal nodes, even if a significantly larger time-step size is chosen, and it can achieve a numerical calculation accuracy as high as the conventional algorithm. The difference scheme of the three dimensional RSG was deduced together with the corresponding updated equations, and a numerical tunnel model with typical hidden disease was presented. The RSG and conventional algorithms were used in the three dimensional simulation. Meanwhile, the comparison of computational efficiency and numerical stability was analyzed, and the calculation result of this model has shown that the RSG algorithm has a quality of higher precision with numerical stability even at a large time-step sizes, which can further facilitate the interpretation of GPR data of typical hidden disease in tunnels.