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Auteur : Grafiati
Publié le 2 septembre 2023

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1

Theillard, Maxime, Frédéric Gibou et David Saintillan. « Sharp numerical simulation of incompressible two-phase flows ». Journal of Computational Physics 391 (août 2019) : 91–118. http://dx.doi.org/10.1016/j.jcp.2019.04.024.

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2

Christafakis, A., J. Alexopoulos et S. Tsangaris. « Modelling of two-phase incompressible flows in ducts ». Applied Mathematical Modelling 33, no 3 (mars 2009) : 1201–12. http://dx.doi.org/10.1016/j.apm.2008.01.014.

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3

Compère, Gaëtan, Emilie Marchandise et Jean-François Remacle. « Transient adaptivity applied to two-phase incompressible flows ». Journal of Computational Physics 227, no 3 (janvier 2008) : 1923–42. http://dx.doi.org/10.1016/j.jcp.2007.10.002.

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4

CAI, LI, JUN ZHOU, FENG-QI ZHOU et WEN-XIAN XIE. « A HYBRID SCHEME FOR THREE-DIMENSIONAL INCOMPRESSIBLE TWO-PHASE FLOWS ». International Journal of Applied Mechanics 02, no 04 (décembre 2010) : 889–905. http://dx.doi.org/10.1142/s1758825110000810.

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We present a hybrid scheme for computations of three-dimensional incompressible two-phase flows. A Poisson-like pressure equation is deduced from the incompressible constraint, i.e., the divergence-free condition of the velocity field, via an extended marker and cell method, and the moment equations in the 3D incompressible Navier–Stokes equations are solved by our 3D semi-discrete Hermite central-upwind scheme. The interface between the two fluids is considered to be the 0.5 level set of a smooth function being a smeared out Heaviside function. Numerical results are offered to verify the desired efficiency and accuracy of our 3D hybrid scheme.
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5

Watanabe, Keiichi. « Compressible–Incompressible Two-Phase Flows with Phase Transition : Model Problem ». Journal of Mathematical Fluid Mechanics 20, no 3 (4 décembre 2017) : 969–1011. http://dx.doi.org/10.1007/s00021-017-0352-3.

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6

Jun, Zhou, Cai Li et Zhou Feng-Qi. « A hybrid scheme for computing incompressible two-phase flows ». Chinese Physics B 17, no 5 (mai 2008) : 1535–44. http://dx.doi.org/10.1088/1674-1056/17/5/001.

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7

Degond, Pierre, Piotr Minakowski et Ewelina Zatorska. « Transport of congestion in two-phase compressible/incompressible flows ». Nonlinear Analysis : Real World Applications 42 (août 2018) : 485–510. http://dx.doi.org/10.1016/j.nonrwa.2018.02.001.

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8

Bhat, Sourabh, et J. C. Mandal. « Contact preserving Riemann solver for incompressible two-phase flows ». Journal of Computational Physics 379 (février 2019) : 173–91. http://dx.doi.org/10.1016/j.jcp.2018.10.039.

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9

Sussman, M., K. M. Smith, M. Y. Hussaini, M. Ohta et R. Zhi-Wei. « A sharp interface method for incompressible two-phase flows ». Journal of Computational Physics 221, no 2 (février 2007) : 469–505. http://dx.doi.org/10.1016/j.jcp.2006.06.020.

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10

Zaspel, Peter, et Michael Griebel. « Solving incompressible two-phase flows on multi-GPU clusters ». Computers & ; Fluids 80 (juillet 2013) : 356–64. http://dx.doi.org/10.1016/j.compfluid.2012.01.021.

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11

Dabonneville, F., N. Hecht, J. Reveillon, G. Pinon et F. X. Demoulin. « A zonal grid method for incompressible two-phase flows ». Computers & ; Fluids 180 (février 2019) : 22–40. http://dx.doi.org/10.1016/j.compfluid.2018.12.016.

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12

Nalimov, V. I. « Two-phase flows of incompressible condensed media and gas ». Journal of Applied Mechanics and Technical Physics 41, no 5 (septembre 2000) : 895–906. http://dx.doi.org/10.1007/bf02468736.

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13

Watanabe, Keiichi. « Strong solutions to compressible–incompressible two-phase flows with phase transitions ». Nonlinear Analysis : Real World Applications 54 (août 2020) : 103101. http://dx.doi.org/10.1016/j.nonrwa.2020.103101.

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14

Chiu, Pao-Hsiung. « A coupled phase field framework for solving incompressible two-phase flows ». Journal of Computational Physics 392 (septembre 2019) : 115–40. http://dx.doi.org/10.1016/j.jcp.2019.04.069.

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15

Chiu, Pao-Hsiung, et Yan-Ting Lin. « A conservative phase field method for solving incompressible two-phase flows ». Journal of Computational Physics 230, no 1 (janvier 2011) : 185–204. http://dx.doi.org/10.1016/j.jcp.2010.09.021.

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16

Chen, Zhangxin. « Numerical Analysis for Two-phase Flow in Porous Media ». Computational Methods in Applied Mathematics 3, no 1 (2003) : 59–75. http://dx.doi.org/10.2478/cmam-2003-0006.

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Abstract In this paper we derive error estimates for finite element approximations for partial differential systems which describe two-phase immiscible flows in porous media. These approximations are based on mixed finite element methods for pressure and velocity and characteristic finite element methods for saturation. Both incompressible and compressible flows are considered. Error estimates of optimal order are obtained.
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17

Rudman, Murray. « One-field equations for two-phase flows ». Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no 2 (octobre 1997) : 149–70. http://dx.doi.org/10.1017/s033427000000878x.

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AbstractA new derivation of the averaged heat and mass transport equations for two-phase flows is presented. A volume averaging technique is used in which averaging is perform over both phases simultaneously in order to derive equations that describe transport the mixture, rather than transport in each phase. The derivation is particularly applicable to incompressible liquid/solid systems in which the two phases are tightly coupled. An example of the numerical solution of the equations is then presented in which a thermally convecting suspension is modelled. It is seen that large-scale instability can result from the interaction of thermal and compositional density gradients.
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18

Watanabe, Keiichi. « Global Solvability of Compressible–Incompressible Two-Phase Flows with Phase Transitions in Bounded Domains ». Mathematics 9, no 3 (28 janvier 2021) : 258. http://dx.doi.org/10.3390/math9030258.

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Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains Ωt+,Ωt−⊂RN, N≥2, where the domains are separated by a sharp compact interface Γt⊂RN−1. We prove a global in time unique existence theorem for such free boundary problem under the assumption that the initial data are sufficiently small and the initial domain of the incompressible fluid is close to a ball. In particular, we obtain the solution in the maximal Lp−Lq-regularity class with 2<p<∞ and N<q<∞ and exponential stability of the corresponding analytic semigroup on the infinite time interval.
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19

Guo, Z., et P. Lin. « A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects ». Journal of Fluid Mechanics 766 (4 février 2015) : 226–71. http://dx.doi.org/10.1017/jfm.2014.696.

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AbstractIn this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier–Stokes equations with additional stress term, Cahn–Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Moreover, some numerical examples including thermocapillary convections in a two-layer fluid system and thermocapillary migration of a drop are computed using a continuous finite element method. The results are compared with the corresponding analytical solutions and the existing numerical results as validations for our model.
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20

Ouafa, Mohamed El. « Navier-Stokes Solvers for Incompressible Single- and Two-Phase Flows ». Communications in Computational Physics 29, no 4 (juin 2021) : 1213–45. http://dx.doi.org/10.4208/cicp.oa-2020-0044.

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21

Sussman, Mark, Emad Fatemi, Peter Smereka et Stanley Osher. « An improved level set method for incompressible two-phase flows ». Computers & ; Fluids 27, no 5-6 (juin 1998) : 663–80. http://dx.doi.org/10.1016/s0045-7930(97)00053-4.

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22

Reuther, Sebastian, et Axel Voigt. « Incompressible two-phase flows with an inextensible Newtonian fluid interface ». Journal of Computational Physics 322 (octobre 2016) : 850–58. http://dx.doi.org/10.1016/j.jcp.2016.07.023.

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23

Saito, Hirokazu, Yoshihiro Shibata et Xin Zhang. « Some Free Boundary Problem for Two-Phase Inhomogeneous Incompressible Flows ». SIAM Journal on Mathematical Analysis 52, no 4 (janvier 2020) : 3397–443. http://dx.doi.org/10.1137/18m1225239.

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24

Hoang, Luan T., Akif Ibragimov et Thinh T. Kieu. « One-dimensional two-phase generalized Forchheimer flows of incompressible fluids ». Journal of Mathematical Analysis and Applications 401, no 2 (mai 2013) : 921–38. http://dx.doi.org/10.1016/j.jmaa.2012.12.055.

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25

Tamellini, Mattia, Nicola Parolini et Marco Verani. « An optimal control problem for two-phase compressible–incompressible flows ». Computers & ; Fluids 172 (août 2018) : 538–48. http://dx.doi.org/10.1016/j.compfluid.2018.03.039.

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26

Sussman, Mark, Ann S. Almgren, John B. Bell, Phillip Colella, Louis H. Howell et Michael L. Welcome. « An Adaptive Level Set Approach for Incompressible Two-Phase Flows ». Journal of Computational Physics 148, no 1 (janvier 1999) : 81–124. http://dx.doi.org/10.1006/jcph.1998.6106.

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27

Qian, Longgen, et Yanhong Wei. « Improved THINC/SW scheme for computing incompressible two-phase flows ». International Journal for Numerical Methods in Fluids 89, no 6 (30 octobre 2018) : 216–34. http://dx.doi.org/10.1002/fld.4690.

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28

Xiao, Yao, Zhong Zeng, Liangqi Zhang, Jingzhu Wang, Yiwei Wang, Hao Liu et Chenguang Huang. « A spectral element-based phase field method for incompressible two-phase flows ». Physics of Fluids 34, no 2 (février 2022) : 022114. http://dx.doi.org/10.1063/5.0077372.

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29

Shen, Jie, et Xiaofeng Yang. « Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows ». SIAM Journal on Numerical Analysis 53, no 1 (janvier 2015) : 279–96. http://dx.doi.org/10.1137/140971154.

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30

Prüss, Jan, et Senjo Shimizu. « Qualitative behaviour of incompressible two-phase flows with phase transitions : The isothermal case ». Proceedings - Mathematical Sciences 127, no 5 (novembre 2017) : 815–31. http://dx.doi.org/10.1007/s12044-017-0365-0.

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31

Ivanov, Aleksandr Vladimirovich, Matvey Viktorovich Kraposhin et Tatiana Gennadyevna Elizarova. « On a new method for regularizing equations two-phase incompressible fluid ». Keldysh Institute Preprints, no 61 (2021) : 1–27. http://dx.doi.org/10.20948/prepr-2021-61.

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This paper presents a new method for the numerical simulation of two-phase incompressible immiscible flows. The methodology is based on the hydrodynamic equations regularization method using the quasi-hydrodynamic approach. Two systems of regularized equations are developed, which differ in terms of velocity regularization. The comparison of the described equations systems and the approbation of the numerical model on two numerical tests are given: dam break problem with the bottom step, for which the experimental data are described (Koshizuka’s experiment), and the cubic drop evolution problem. The latter problem is a model one with artificially specified parameters that demonstrates the effects of surface tension. A numerical model of two-phase flows is implemented in the open-source platform OpenFOAM using the finite volume method.
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32

G. Gal, Ciprian, et Maurizio Grasselli. « Longtime behavior for a model of homogeneous incompressible two-phase flows ». Discrete & ; Continuous Dynamical Systems - A 28, no 1 (2010) : 1–39. http://dx.doi.org/10.3934/dcds.2010.28.1.

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33

Jiang, Jie, Yinghua Li et Chun Liu. « Two-phase incompressible flows with variable density : An energetic variational approach ». Discrete & ; Continuous Dynamical Systems - A 37, no 6 (2017) : 3243–84. http://dx.doi.org/10.3934/dcds.2017138.

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34

Bhat, Sourabh P., et J. C. Mandal. « An improved HLLC-type solver for incompressible two-phase fluid flows ». Computers & ; Fluids 244 (août 2022) : 105570. http://dx.doi.org/10.1016/j.compfluid.2022.105570.

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35

Gal, Ciprian G., et T. Tachim Medjo. « Regularized family of models for incompressible Cahn–Hilliard two-phase flows ». Nonlinear Analysis : Real World Applications 23 (juin 2015) : 94–122. http://dx.doi.org/10.1016/j.nonrwa.2014.11.005.

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36

Fahsi, Adil, et Azzeddine Soulaïmani. « Numerical investigations of the XFEM for solving two-phase incompressible flows ». International Journal of Computational Fluid Dynamics 31, no 3 (16 mars 2017) : 135–55. http://dx.doi.org/10.1080/10618562.2017.1322200.

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37

Reusken, Arnold, et Trung Hieu Nguyen. « Nitsche’s Method for a Transport Problem in Two-phase Incompressible Flows ». Journal of Fourier Analysis and Applications 15, no 5 (29 août 2009) : 663–83. http://dx.doi.org/10.1007/s00041-009-9092-y.

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38

Huang, Ziyang, Guang Lin et Arezoo M. Ardekani. « A mixed upwind/central WENO scheme for incompressible two-phase flows ». Journal of Computational Physics 387 (juin 2019) : 455–80. http://dx.doi.org/10.1016/j.jcp.2019.02.043.

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39

Hachem, E., M. Khalloufi, J. Bruchon, R. Valette et Y. Mesri. « Unified adaptive Variational MultiScale method for two phase compressible–incompressible flows ». Computer Methods in Applied Mechanics and Engineering 308 (août 2016) : 238–55. http://dx.doi.org/10.1016/j.cma.2016.05.022.

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40

Yang, Rihua, Heng Li et Aiming Yang. « A HLLC-type finite volume method for incompressible two-phase flows ». Computers & ; Fluids 213 (décembre 2020) : 104715. http://dx.doi.org/10.1016/j.compfluid.2020.104715.

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41

Ki, Hyungson. « Level set method for two-phase incompressible flows under magnetic fields ». Computer Physics Communications 181, no 6 (juin 2010) : 999–1007. http://dx.doi.org/10.1016/j.cpc.2010.02.002.

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42

Lehrenfeld, Christoph. « Nitsche-XFEM for a transport problem in two-phase incompressible flows ». PAMM 11, no 1 (décembre 2011) : 613–14. http://dx.doi.org/10.1002/pamm.201110296.

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43

Gao, Huicai, Jisheng Kou, Shuyu Sun et Xiuhua Wang. « Thermodynamically consistent modeling of two-phase incompressible flows in heterogeneous and fractured media ». Oil & ; Gas Science and Technology – Revue d’IFP Energies nouvelles 75 (2020) : 32. http://dx.doi.org/10.2516/ogst/2020024.

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Numerical modeling of two-phase flows in heterogeneous and fractured media is of great interest in petroleum reservoir engineering. The classical model for two-phase flows in porous media is not completely thermodynamically consistent since the energy reconstructed from the capillary pressure does not involve the ideal fluid energy of both phases and attraction effect between two phases. On the other hand, the saturation may be discontinuous in heterogeneous and fractured media, and thus the saturation gradient may be not well defined. Consequently, the classical phase-field models can not be applied due to the use of diffuse interfaces. In this paper, we propose a new thermodynamically consistent energy-based model for two-phase flows in heterogeneous and fractured media, which is free of the gradient energy. Meanwhile, the model inherits the key features of the traditional models of two-phase flows in porous media, including relative permeability, volumetric phase velocity and capillarity effect. To characterize the capillarity effect, a logarithmic energy potential is proposed as the free energy function, which is more realistic than the commonly used double well potential. The model combines with the discrete fracture model to describe two-phase flows in fractured media. The popularly used implicit pressure explicit saturation method is used to simulate the model. Finally, the experimental verification of the model and numerical simulation results are provided.
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44

Li, Wei, Yihui Ma, Xiaopei Liu et Mathieu Desbrun. « Efficient kinetic simulation of two-phase flows ». ACM Transactions on Graphics 41, no 4 (juillet 2022) : 1–17. http://dx.doi.org/10.1145/3528223.3530132.

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Real-life multiphase flows exhibit a number of complex and visually appealing behaviors, involving bubbling, wetting, splashing, and glugging. However, most state-of-the-art simulation techniques in graphics can only demonstrate a limited range of multiphase flow phenomena, due to their inability to handle the real water-air density ratio and to the large amount of numerical viscosity introduced in the flow simulation and its coupling with the interface. Recently, kinetic-based methods have achieved success in simulating large density ratios and high Reynolds numbers efficiently; but their memory overhead, limited stability, and numerically-intensive treatment of coupling with immersed solids remain enduring obstacles to their adoption in movie productions. In this paper, we propose a new kinetic solver to couple the incompressible Navier-Stokes equations with a conservative phase-field equation which remedies these major practical hurdles. The resulting two-phase immiscible fluid solver is shown to be efficient due to its massively-parallel nature and GPU implementation, as well as very versatile and reliable because of its enhanced stability to large density ratios, high Reynolds numbers, and complex solid boundaries. We highlight the advantages of our solver through various challenging simulation results that capture intricate and turbulent air-water interaction, including comparisons to previous work and real footage.
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45

Behrangi, Farhang, Mohammad Ali Banihashemi, Masoud Montazeri Namin et Asghar Bohluly. « FGA-MMF method for the simulation of two-phase flows ». Engineering Computations 35, no 3 (8 mai 2018) : 1161–82. http://dx.doi.org/10.1108/ec-03-2017-0076.

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Purpose This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model. Design/methodology/approach The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used. Findings This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results. Research limitations/implications The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow. Originality/value The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.
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46

Shen, Jie, et Xiaofeng Yang. « Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows ». Chinese Annals of Mathematics, Series B 31, no 5 (25 août 2010) : 743–58. http://dx.doi.org/10.1007/s11401-010-0599-y.

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47

Shah, Abdullah, Sadia Saeed et L. Yuan. « An Artificial Compressibility Method for 3D Phase-Field Model and its Application to Two-Phase Flows ». International Journal of Computational Methods 14, no 05 (6 janvier 2017) : 1750059. http://dx.doi.org/10.1142/s0219876217500591.

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In this work, a numerical scheme based on artificial compressibility formulation of a phase-field model is developed for simulating two-phase incompressible flow problems. The coupled nonlinear systems composed of the incompressible Navier–Stokes equations and volume preserving Allen–Cahn-type phase-field equation are recast into conservative form with source terms, which are suited to implement high-resolution schemes originally developed for hyperbolic conservation laws. The Boussinesq approximation is used to account for the buoyancy effect in flow with small density difference. The fifth-order weighted essentially nonoscillatory (WENO) scheme is used for discretizing the convective terms while dual-time stepping (DTS) technique is used for obtaining time accuracy at each physical time step. Beam–Warming approximate factorization scheme is utilized to obtain block tridiagonal system of equations in each spatial direction. The alternating direction implicit (ADI) algorithm is used to solve the resulting system of equations. The performance of the method is demonstrated by its application to some 2D and 3D benchmark viscous two-phase flow problems.
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48

TAKADA, NAOKI, et AKIO TOMIYAMA. « NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING ». International Journal of Modern Physics C 18, no 04 (avril 2007) : 536–45. http://dx.doi.org/10.1142/s0129183107010772.

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For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.
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49

Son, Gihun, et Nahmkeon Hur. « A Level Set Formulation for Incompressible Two-Phase Flows on Nonorthogonal Grids ». Numerical Heat Transfer, Part B : Fundamentals 48, no 3 (septembre 2005) : 303–16. http://dx.doi.org/10.1080/10407790590959762.

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50

Frachon, Thomas, et Sara Zahedi. « A cut finite element method for incompressible two-phase Navier–Stokes flows ». Journal of Computational Physics 384 (mai 2019) : 77–98. http://dx.doi.org/10.1016/j.jcp.2019.01.028.

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