A Finite‐Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

Abstract

AbstractHeterogeneous media is a kind of multi‐scale media. The scale of the fracture reservoir could reach up to millimeter. Simulating a fractured carbonate model with finite‐difference method is calling for the same scale of sample steps. A finite‐difference method with high power of grid steps variation is presented here. Spatial and temporal sampling steps can be optimized according to material properties and model geometry. The ratio of grid steps could reach up to hundreds or more. We improve the method of numerical grid division in order to add more flexibility and efficiency to finite‐difference method with grid variation. The numerical results support that the method can describe heterogeneous media on millimeter scale accurately with efficiency, and the property made the method suitable for modeling cavity or fractured carbonate reservoirs.