Numerical solution of a stationary filtration problem of viscous fluid in a piecewise homogeneous porous medium by applying the boundary integral equation method

A numerical method based on boundary integral equations is constructed for simulating three-dimensional stationary filtration flow through a homogeneous porous medium with homogeneous inclusions. The flow is simulated taking into account the viscosity of the fluid. Boundary integral equations are written on the outer boundary of the flow region and on the boundary surfaces of the inclusions. The integral equations are solved numerically using the methods of piecewise constant approximation and collocations. The numerical method is tested on model problems.