Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow

Baňas, Ľubomír; Nürnberg, Robert

doi:10.1051/m2an/2016048

Cited by 14 publications

(23 citation statements)

References 30 publications

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“…The latter subject, typically involving breakup and coalescence such as fluid jets and droplets as well as fluid mixing and other interfacial phenomena, has become particularly important in microfluidics and micro-process engineering, see [354,427] for reviews on the various numerical approaches. Phase field modeling of multiphase flows has been developed by a number of groups along with the development and numerical analysis, see, for instance [2,315,25,29,140,225,189,236,313] and the references cited therein. Various phase field based simulations of drop formation in microfluidic channels have been carried out, see for example [444].…”

Section: Fluid and Solid Mechanicsmentioning

confidence: 99%

The phase field method for geometric moving interfaces and their numerical approximations

Feng

2020

Handbook of Numerical Analysis

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This chapter surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical methods and their analyses, the chapter presents a holistic overview about the main ideas of phase field modeling, its mathematical foundation, and relationships between the phase field formalism and other mathematical formalisms for geometric moving interface problems, as well as the current state-of-the-art of numerical approximations of various phase field models with an emphasis on discussing the main ideas of numerical analysis techniques. The chapter also reviews recent development on adaptive grid methods and various applications of the phase field modeling and their numerical methods in materials science, fluid mechanics, biology and image science. Key words and phrases. Phase field method, geometric law, curvature-driven flow, geometric nonlinear PDEs, finite difference methods, finite element methods, spectral methods, discontinuous Galerkin methods, adaptivity, coarse and fine error estimates, convergence of numerical interfaces, nonlocal and stochastic phase field models, microstructure evolution, biology and image science applications.

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Section: Fluid and Solid Mechanicsmentioning

confidence: 99%

The phase field method for geometric moving interfaces and their numerical approximations

Feng

2020

Handbook of Numerical Analysis

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“…where we have used equations (3c) and (5). Let T = −pI + µD(u) denote the stress tensor, where I is the identity tensor.…”

Section: N-phase Energy Balance and Energy-stable Boundary Conditionsmentioning

confidence: 99%

“…The results demonstrate that the proposed method can serves as an accurate and reliable tool for the investigation of multi-phase flow problems in unbounded domains. Note that all numerical simulations presented here are performed by using the volume fractions c i (1 ≤ i ≤ N − 1) as the order parameters, as defined in (5).…”

Section: Representative Numerical Examplesmentioning

confidence: 99%

Multiphase flows of N immiscible incompressible fluids: An outflow/open boundary condition and algorithm

Yang

Dong

2018

Journal of Computational Physics

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We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of N (N 2) immiscible incompressible fluids in domains involving outflows or open boundaries. These boundary conditions are devised based on the properties of energy stability and reduction consistency. The energy stability property ensures that the contributions of these boundary conditions to the energy balance will not cause the total energy of the N-phase system to increase over time. Therefore, these open/outflow boundary conditions are very effective in overcoming the backflow instability in multiphase systems. The reduction consistency property ensures that if some fluid components are absent from the N-phase system then these Nphase boundary conditions will reduce to those corresponding boundary conditions for the equivalent smaller system. Our numerical algorithm for the proposed boundary conditions together with the Nphase governing equations involves only the solution of a set of de-coupled individual Helmholtz-type equations within each time step, and the resultant linear algebraic systems after discretization involve only constant and time-independent coefficient matrices which can be pre-computed. Therefore, the algorithm is computationally very efficient and attractive. We present extensive numerical experiments for flow problems involving multiple fluid components and inflow/outflow boundaries to test the proposed method. In particular, we compare in detail the simulation results of a three-phase capillary wave problem with Prosperetti's exact physical solution and demonstrate that the method developed herein produces physically accurate results.

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“…Multiphase problems involving three or more fluid components have attracted a growing interest, and a number of researchers have contributed to the advance of this field; see e.g. [28,6,26,7,27,24,12,5,15,9,39,3,37], among others. Among the past studies, a handful of phase field models (e.g.…”

Section: Introductionmentioning

confidence: 99%

Multiphase flows of N immiscible incompressible fluids: A reduction-consistent and thermodynamically-consistent formulation and associated algorithm

Dong

2018

Journal of Computational Physics

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We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of N (N 2) immiscible incompressible fluids with different physical properties (densities, viscosities, and pair-wise surface tensions). By reduction consistency we refer to the property that if only a set of M (1 M N −1) fluids are present in the system then the N-phase governing equations and boundary conditions will exactly reduce to those for the corresponding M -phase system. By theromdynamic consistency we refer to the property that the formulation honors the thermodynamic principles. Our N-phase formulation is developed based on a more general method that allows for the systematic construction of reductionconsistent formulations, and the method suggests the existence of many possible forms of reductionconsistent and thermodynamically consistent N-phase formulations. Extensive numerical experiments have been presented for flow problems involving multiple fluid components and large density ratios and large viscosity ratios, and the simulation results are compared with the physical theories or the available physical solutions. The comparisons demonstrate that our method produces physically accurate results for this class of problems.

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Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow

Cited by 14 publications

References 30 publications

The phase field method for geometric moving interfaces and their numerical approximations

The phase field method for geometric moving interfaces and their numerical approximations

Multiphase flows of N immiscible incompressible fluids: An outflow/open boundary condition and algorithm

Multiphase flows of N immiscible incompressible fluids: A reduction-consistent and thermodynamically-consistent formulation and associated algorithm

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