Advanced alternate triangular method of numerical solution of spatial three-dimensional problems of two-phase filtration of incompressible fluid

модели фильтрации Баклея , Buckley - Leverett filtration models, two-phase incompressible liquid, difference schemes, iteration alternate triangular method, iteration parameters, двухфазная несжимаемая жидкость, разностные схемы, итерационный попеременно-треугольный метод, итерационные параметры

1. Aziz, K., Settary, E. Matematicheskoe modelirovanie plastovykh system. [Mathematical modeling of tabular systems.] Moscow; Izhevsk: Institute of Computer Science, 2004, 416 p. (in Russian).

2. Konovalov, А.N. Zadachi fil'tratsii mnogofaznoy neszhimaemoy zhidkosti. [Filtering problems of multiple incompressible fluids.] Novosibirsk: Nauka, 1988, 166 p. (in Russian).

3. Vabishchevich, P.N. Yavno-neyavnye vychislitel'nye algoritmy dlya zadach mnogofaznoy fil'tratsii. [Explicitimplicit numerical algorithms for porous media multiphase flow problems.] Mathematical Models and Computer Simulations, 2010, vol. 22, no. 4, pp. 118–128 (in Russian).

4. Sukhinov, А.I. Modifitsirovannyy poperemenno-treugol'nyy metod dlya zadach teploprovodnosti i fil'tratsii. [Modified alternating triangular method for heat conduction problems and filtering.] Vychislitel'nye sistemy i algoritmy. [Computation systems and algorithms.] Rostov-on-Don: Rostov State University, 1984, pp. 52–59 (in Russian).

5. Sukhinov, А.I. Dvumernye skhemy rasshchepleniya i nekotorye ikh prilozheniya. [Two-dimensional splitting schemes and some of their applications.] Moscow: MAKS Press, 2005, 408 p. (in Russian).

6. Sukhinov, А.I., Chistyakov, A.E., Shishenya, A.V. Modifikatsiya metoda minimal'nykh popravok dlya resheniya setochnykh uravneniy s nesamosopryazhennym operatorom. [Modification of minimal residuals iterative method for solving grid equations with nonselfadjoint operators.] Izvestiya SFedU. Engineering Sciences, 2013, no. 4,pp. 194–202 (in Russian).

7. Sukhinov, А.I., Chistyakov, A.E. Adaptivnyy poperemenno-treugol'nyy metod dlya resheniya setochnykh uravneniy s nesamosopryazhennym operatorom. [Adaptive analog- SSOR iterative method for solving grid equations with nonselfadjoint operators.] Mathematical Models and Computer Simulations, 2012, vol. 24, no. 1, pp. 3–20 (in Russian).

8. Samarsky, А.А., Nikolaev, E.S. Metody resheniya setochnykh uravneniy. [Solution methods of finite-difference equations.] Moscow: Nauka, 1978, 592 p. (in Russian).

9. Trapeznikova, M., et al. Two-Phase Porous Media Flow Simulation on Hybrid Cluster. Lecture Notes in Computer Science, 2012, no. 7116, pp. 644–651.

10. Berveno, Е.V., Kalinkin, A.A., Laevskii, Y.M. Fil'tratsiya dvukhfaznoy zhidkosti v neodnorodnoy srede na komp'yuterakh s raspredelennoy pamyat'yu. [Two-phase fluid filtration in nonuniform media on clusters.] Tomsk State University Journal of Mathematics and Mechanics, 2014, no. 4 (30), pp. 57–62 (in Russian).

11. Laevskii, Y.M., Litvinenko, S.A. Ob odnom vychislitel'nom algoritme resheniya uravneniy Bakleya — Leveretta. [On a numerical algorithm for solving the Backley- Laverett equations.] Journal of Applied and Industrial Mathematics, 2013, vol. 16, no. 3, pp. 106–115 (in Russian).

12. Dushin, V.R., et al. Mathematical modeling of flows in porous media. WSEAS Transactions on Fluid Mechanics,

13. 2014, vol. 9, pp. 166–130.