Numerical Investigation of Nonlinear Filtration Problems of High-Viscosity Fluids in Porous Media

Abstract

We consider a steady process of filtration of the incompressible high-viscosity fluid, following non-linear filtration law. Generalized statement of this problem is formulated in the form of operator equation with monotone operator in Banach space. To solve the operator equation, we suggest iterative method that does not require the inversion of the original operator. Each step of the iterative process can essentially be reduced to the solution of the boundary-value problem for the Laplace operator. This method was realized numerically. The numerical experiments made for the model problems confirmed the efficiency of the iterative method.