Ключевые слова: алгоритмы методов Монте - Карло, модель фильтрации, насыщенность, давление, нелинейный закон Дарси, вероятностно-разностный метод, начально-краевая задача
Annotation
Numerical solution the one musket - Leverett's model by Monte Carlo methods and probability difference method. Shakenov Kanat K., Doctor of Physical and Mathematical Science, Professor, Sultanova Marzhan S., PhD post-graduate, Al-Farabi Kazakh National University, Kazakhstan, 050040, Almaty, Al-Farabi avenue, 71, e-mail: marzhan.ss@mail.ru. Tastanov Meirambek G., Candidate of Physical and Mathematical Science, Associate Professor, A. Baitursynov KSU, Kazakhstan, 110000, Kostanai, Baitursynov street, 47, e-mail: tastao@mail.ru
The goal of the paper is to develop and construct algorithms of Monte Carlo methods and probability difference methods for the solution of one liquid filtration model that obeys to non-Newtonian laws. Generalizations of Darcy laws for non-compressible components of the mixture for nonlinear law of environment resistance can be produced by analogy with poly-velocity model of Navier - Stocks by means of introducing forces of interaction of these components or by analogy with non-uniform liquid by means of dependences of phase penetrability's on pressure gradient of the components. We consider two forms of non-linear Darcy laws, to which Musket - Leverett's model obeys. This model describes process of filtration for two liquids in porous environment by system of equations with respect to pressure and saturation. For this system of equations we set up an initial boundary value problems and solved by Monte Carlo methods and probability difference method.
Keywords: Monte Carlo methods algorithms, filtration model, saturation, pressure, non-linear Darcy laws, probability difference method, initial boundary value problem