Modelling Flow through Heterogeneous Porous Media with Boundary Integrals using Higher-Order Surface Singularities

Numerical modelling of heterogeneous porous media has received attention at a variety of scales from pore dimensions to those of hundreds of meters. Most of the approaches to predict the behaviour of flow have focussed on enhancements to established finite difference schemes (e.g., local grid refinement, multi-grid methods). Although finite difference schemes have many advantages, in fine grids they are difficult to apply properly to curved surfaces with Neumann boundary conditions, which occur at the boundary between media of different permeability and they appear very difficult to use with multiple heterogeneities. In such circumstances boundary conditions can often be expressed using boundary integral equations, and solutions by powerful boundary integral equation methods can be applied.