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On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types
Some attempts to couple distinct fluid models
1. | EDF R&D, MFEE, 6, quai Watier, Chatou, 78400, France, France |
[1] |
Christophe Chalons. Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows. Networks and Heterogeneous Media, 2010, 5 (3) : 507-524. doi: 10.3934/nhm.2010.5.507 |
[2] |
Qinglong Zhang. Delta waves and vacuum states in the vanishing pressure limit of Riemann solutions to Baer-Nunziato two-phase flow model. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3235-3258. doi: 10.3934/cpaa.2021104 |
[3] |
Theodore Tachim Medjo. A two-phase flow model with delays. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3273-3294. doi: 10.3934/dcdsb.2017137 |
[4] |
Stefan Berres, Ricardo Ruiz-Baier, Hartmut Schwandt, Elmer M. Tory. An adaptive finite-volume method for a model of two-phase pedestrian flow. Networks and Heterogeneous Media, 2011, 6 (3) : 401-423. doi: 10.3934/nhm.2011.6.401 |
[5] |
Eberhard Bänsch, Steffen Basting, Rolf Krahl. Numerical simulation of two-phase flows with heat and mass transfer. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2325-2347. doi: 10.3934/dcds.2015.35.2325 |
[6] |
Ciprian G. Gal, Maurizio Grasselli. Longtime behavior for a model of homogeneous incompressible two-phase flows. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 1-39. doi: 10.3934/dcds.2010.28.1 |
[7] |
Jie Jiang, Yinghua Li, Chun Liu. Two-phase incompressible flows with variable density: An energetic variational approach. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3243-3284. doi: 10.3934/dcds.2017138 |
[8] |
Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete and Continuous Dynamical Systems - S, 2021, 14 (11) : 3973-3987. doi: 10.3934/dcdss.2020467 |
[9] |
T. Tachim Medjo. Averaging of an homogeneous two-phase flow model with oscillating external forces. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3665-3690. doi: 10.3934/dcds.2012.32.3665 |
[10] |
Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. Global existence for a two-phase flow model with cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 957-979. doi: 10.3934/dcdsb.2019198 |
[11] |
Theodore Tachim-Medjo. Optimal control of a two-phase flow model with state constraints. Mathematical Control and Related Fields, 2016, 6 (2) : 335-362. doi: 10.3934/mcrf.2016006 |
[12] |
Changyan Li, Hui Li. Well-posedness of the two-phase flow problem in incompressible MHD. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5609-5632. doi: 10.3934/dcds.2021090 |
[13] |
Alberto Bressan, Anders Nordli. The Riemann solver for traffic flow at an intersection with buffer of vanishing size. Networks and Heterogeneous Media, 2017, 12 (2) : 173-189. doi: 10.3934/nhm.2017007 |
[14] |
Jan Prüss, Yoshihiro Shibata, Senjo Shimizu, Gieri Simonett. On well-posedness of incompressible two-phase flows with phase transitions: The case of equal densities. Evolution Equations and Control Theory, 2012, 1 (1) : 171-194. doi: 10.3934/eect.2012.1.171 |
[15] |
Barbara Lee Keyfitz, Richard Sanders, Michael Sever. Lack of hyperbolicity in the two-fluid model for two-phase incompressible flow. Discrete and Continuous Dynamical Systems - B, 2003, 3 (4) : 541-563. doi: 10.3934/dcdsb.2003.3.541 |
[16] |
Anna Kaźmierczak, Jan Sokolowski, Antoni Zochowski. Drag minimization for the obstacle in compressible flow using shape derivatives and finite volumes. Mathematical Control and Related Fields, 2018, 8 (1) : 89-115. doi: 10.3934/mcrf.2018004 |
[17] |
Michela Eleuteri, Elisabetta Rocca, Giulio Schimperna. On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2497-2522. doi: 10.3934/dcds.2015.35.2497 |
[18] |
Clément Cancès. On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types. Networks and Heterogeneous Media, 2010, 5 (3) : 635-647. doi: 10.3934/nhm.2010.5.635 |
[19] |
Hirokazu Saito, Xin Zhang. Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4609-4643. doi: 10.3934/dcds.2021051 |
[20] |
K. Domelevo. Well-posedness of a kinetic model of dispersed two-phase flow with point-particles and stability of travelling waves. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 591-607. doi: 10.3934/dcdsb.2002.2.591 |
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