An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media

Liu, Chen; Frank, Florian; Thiele, Christopher; Alpak, Faruk O.; Berg, Steffen; Chapman, Walter G.; Rivière, Béatrice

doi:10.1016/j.jcp.2019.108948

Cited by 25 publications

(16 citation statements)

References 36 publications

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“…Note that the initial planar interface develops into a protruded interface due to the underlying velocity field. The extent of the protrusion can vary depending on the choice of Pe c , as has been observed in [22]. The final surfactant profiles for various combinations of α 3 and α 4 are shown in Figure 10.…”

Section: Flow Through a Cylindermentioning

confidence: 65%

“…In a recent series of works [10,9,22], a diffusive-interface framework was considered for an immiscible two-phase flows at the pore-scale in rock samples. The location of the two-phases in the pore space of the rock is expressed in terms of an order parameter, which may be defined as the difference between mass fractions.…”

Section: Introductionmentioning

confidence: 99%

“…An interior penalty discontinuous Galerkin (IPDG) scheme was proposed to solve the system, while a temporal semi-implicit convex-concave splitting ensured the scheme to be unconditionally energy stable [10]. The coupled Cahn-Hilliard-Navier-Stokes problem has received much attention recently and several numerical methods have been employed to solve this problem, namely finite element methods and mixed element methods in [8,2,12], finite volume methods [18] and discontinuous Galerkin methods [11,22].…”

Section: Introductionmentioning

confidence: 99%

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A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

Ray¹,

Liu²,

Rivière³

2020

Preprint

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A numerical method using discontinuous polynomial approximations is formulated for solving a phase-field model of two immiscible fluids with a soluble surfactant. The scheme recovers the Langmuir adsorption isotherms at equilibrium. Simulations of spinodal decomposition, flow through a cylinder and flow through a sequence of pore throats show the dynamics of the flow with and without surfactant. Finally the numerical method is used to simulate fluid flows in the pore space of Berea sandstone obtained by micro-CT imaging.

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Section: Flow Through a Cylindermentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

Ray¹,

Liu²,

Rivière³

2020

Preprint

Self Cite

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“…Driven by applications in the analysis of lateral organization of plasma membranes (see [45,46] for more context), we adopt this new model to simulate two-phase flow dynamics on arbitrary-shaped closed smooth surfaces. While there exist many computational studies of multi-component fluid flows in planar and volumetric domains (see, e.g., [19,28,31,44,47] for some recent works), the number of papers where NSCH systems are treated on manifolds is limited. This can be explained by the fact that solving equations numerically on general surfaces poses additional difficulties that are related to the discretization of tangential differential operators and the approximate recovery of (possibly) complex shapes.…”

Section: Introductionmentioning

confidence: 99%

A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow

Palzhanov¹,

Zhiliakov²,

Quaini³

et al. 2021

Preprint

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The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by applications in biomembrane studies, the model is written for tangential flows of fluids constrained to a surface and consists of (surface) Navier-Stokes-Cahn-Hilliard type equations. We apply an unfitted finite element method to discretize the system and introduce a fully discrete time-stepping scheme with the following properties: (i) the scheme decouples the fluid and phase-field equation solvers at each time step, (ii) the resulting two algebraic systems are linear, and (iii) the numerical solution satisfies the same stability bound as the solution of the original system under some restrictions on the discretization parameters. Numerical examples are provided to demonstrate the stability, accuracy, and overall efficiency of the approach. Our computational study of several two-phase surface flows reveals some interesting dependencies of flow statistics on the geometry.

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“…The model that belongs to the class of diffuse interface or phase-field methods, has been used in physics, chemistry, biology, and engineering fields. In recent years, driven by the major developments of numerical algorithms and by increased availability of computational resources, direct numerical simulation of Cahn-Hilliard-Navier-Stokes equations has become increasingly popular [1,14,16,25,27,30].…”

Section: Introductionmentioning

confidence: 99%

A priori Error Analysis of a Discontinuous Galerkin MethodforCahn–Hilliard–Navier–StokesEquations

sci¹

2020

CSIAM

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In this paper, we analyze an interior penalty discontinuous Galerkin method for solving the coupled Cahn-Hilliard and Navier-Stokes equations. We prove unconditional unique solvability of the discrete system, and we derive stability bounds without any restrictions on the chemical energy density function. The numerical solutions satisfy a discrete energy dissipation law and mass conservation laws. Convergence of the method is obtained by obtaining optimal a priori error estimates.

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An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media

Cited by 25 publications

References 36 publications

A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow

A priori Error Analysis of a Discontinuous Galerkin MethodforCahn–Hilliard–Navier–StokesEquations

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