PARALLEL NUMERICAL METHOD OF AN INVERSE PROBLEM OF DOUBLE-PHASED FILTRATION
DOI:
https://doi.org/10.32010/26166127.2019.2.1.75.81Keywords:
Open MP technology, double-phased filtration, displacement, mathematical modellingAbstract
Was investigated the process of the displacement of oil with water in the horizontally located two-dimensional layer, which is described with the double-phased filtration model of incompressible liquid in non-deformable porous media. Within this model was set inverse problem for the definition flow rate of exploitative wells. Meanwhile, as additional conditions are set downhole pressure in injection wells. For the numerical solution of the problem, firstly was conducted discretization by time. As a result original problem comes down to two independent problems which are solved sequentially in each layer of time: the inverse problem for the definition of pressure distribution and flow rate of exploitative wells and forward problem for the definition of saturation of displacing phase. For the solution of the forward problem was offered particular fission, which gives an opportunity parallelization of received differential problems. In the base of the offered numerical method were carried out experimental results for model tasks. For parallelization of computing, processes was applied Open MP technology.
Downloads
References
[1] Masket, M. (2004). Techenie odnorodnyh zhidkostej v poristoj srede. Moskva-Izhevsk: Institut komp'juternyh issledovanij, 628.
[2] Konovalov, A. N. (1988). Zadachi fil'tracii mnogofaznoj neszhimaemoj zhidkosti. Nauka. Sib. otd-nie.
[3] Aziz, H., Settari, Je., Korolev, A. V., Kestner, V. P., & Maksimov, M. M. (2004). Matematicheskoe modelirovanie plastovyh sistem. Reguljarnaja i haoticheskaja dinamika| Izhevskij institut komp'juternyh issledovanij.
[4] Samarskij, A. A., & Vabishchevich, P. N. (2004). Chislennye metody reshenija obratnyh zadach matematicheskoj fiziki. URSS.
[5] Borukhov, V. T., & Vabishchevich, P. N. (2000). Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation. Computer physics communications, 126(1-2), 32-36.
[6] Vabishchevich, P. N., Vasil'ev, V. I., & Vasil'eva, M. V. (2015). Vychislitel'naja identifikacija pravoj chasti parabolicheskogo uravnenija. Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki, 55(6), 1020-1027.
[7] Vabishchevich, P. N., Vasil'ev, V. I., Vasil'eva, M. V., & Nikiforov, D. Ja. (2015). Chislennoe reshenie odnoj obratnoj zadachi fil'tracii. Uchenye zapiski Kazanskogo universiteta. Serija Fiziko-matematicheskie nauki, 157(4).
[8] Gamzaev, K. M. (2015). Modeling nonstationary nonlinear-viscous liquid flows through a pipeline. Journal of Engineering Physics and Thermophysics, 88(2), 480-485.
[9] Gamzaev, K. M. (2017). Numerical solution of combined inverse problem for generalized Burgers equation. Journal of Mathematical Sciences, 221(6), 833-839.
[10] Deng, Z. C., Qian, K., Rao, X. B., Yang, L., & Luo, G. W. (2015). An inverse problem of identifying the source coefficient in a degenerate heat equation. Inverse Problems in Science and Engineering, 23(3), 498-517.
[11] Marchuk, G. I. (1982). Matematicheskoe modelirovanie v probleme okruzhajushhej sredy. " Nauka," Glav. red. fiziko-matematicheskoj lit-ry.
