Numerical methods for determination the boundaries of unrecovered visco-plastic oil

Abstract

In the present work, numerical methods are proposed for solving the problem of determining the boundaries of the unrecovered visco-plastic oil. This problem reduces to a stationary filtration problem for an incompressible fluid with an effective multi-valued law consisting in finding pressure fields and filtration velocity that satisfy the continuity equation and boundary conditions. A generalized formulation is formulated for pressure in the form of a mixed variational inequality with non-differentiable functional. To solve the variational inequality, an iterative splitting method is proposed that does not require inversion of the original operator. For the numerical implementation of this iterative method, finite element approximations of the variational inequality and the iteration method were constructed. A software package was developed in the Matlab environment. For model problems, numerical experiments were carried out for various initial data. The experimental results indicate the effectiveness of the iterative method.