The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows with Phase Change

Jamet, Dominique; Lebaigue, Olivier; Coutris, N.; Delhaye, J. M.

doi:10.1006/jcph.2000.6692

Cited by 252 publications

(160 citation statements)

References 31 publications

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“…It relies more on minimal energy consideration and can eliminate parasitic currents down to machine precision. Note, that this approach is applied in the context of diffuse interface and second gradient method [17].…”

Section: Introductionmentioning

confidence: 99%

On stability condition for bifluid flows with surface tension: Application to microfluidics

Galusinski

Vigneaux

2008

Journal of Computational Physics

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Models for incompressible immiscible bifluid flows with surface tension are here considered. Since Brackbill, Kothe and Zemach (J. Comput. Phys. 100, pp 335-354, 1992) introduced the Continuum Surface Force (CSF) method, many methods involved in interface tracking or capturing are based on this reference work. Particularly, the surface tension term is discretized explicitly and therefore, a stability condition is induced on the computational time step. This constraint on the time step allows the containment of the amplification of capillary waves along the interface and puts more emphasis on the terms linked with the density in the Navier-Stokes equation (i. e. unsteady and inertia terms) rather than on the viscous terms. Indeed, the viscosity does not appear, as a parameter, in this stability condition.We propose a new stability condition which takes into account all fluid characteristics (density and viscosity) and for which we present a theoretical estimation. We detail the analysis which is based on a perturbation study -with capillary wave -for which we use energy estimate on the induced perturbed velocity. We validate our analysis and algorithms with numerical simulations of microfluidic flows using a Level Set method, namely the exploration of different mixing dynamics inside microdroplets.

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Section: Introductionmentioning

confidence: 99%

On stability condition for bifluid flows with surface tension: Application to microfluidics

Galusinski

Vigneaux

2008

Journal of Computational Physics

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“…Therefore, this model opens the possibility to solve vexing problems in computational mechanics such as for example, cavitation, film and nucleate boiling or the phasechange-driven implosion of thin structures (Bueno et al, 2014). The Navier-Stokes-Korteweg equations are rather new in the field, but there are interesting works of theoretical (Dunn and Serrin, 1986) and computational nature (Gomez et al, 2010b;Liu et al, 2013Liu et al, , 2015Tian et al, 2015;Giesselmann et al, 2014;Jamet et al, 2001). Our point of departure to derive the Navier-Stokes-Korteweg equations are classical balance laws for mass, linear momentum, angular momentum and energy, which may be written as followṡ…”

Section: Mechano-biological Mixtures: Phase-field Tumor Growth Theorymentioning

confidence: 99%

Computational Phase‐Field Modeling

Gómez

Zee

2017

Encyclopedia of Computational Mechanics Second Edition

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Phase-field modeling is emerging as a promising tool for the treatment of problems with interfaces. The classical description of interface problems requires the numerical solution of partial differential equations on moving domains in which the domain motions are also unknowns. The computational treatment of these problems requires moving meshes and is very difficult when the moving domains undergo topological changes. Phase-field modeling may be understood as a methodology to reformulate interface problems as equations posed on fixed domains. In some cases, the phase-field model may be shown to converge to the moving-boundary problem as a regularization parameter tends to zero, which shows the mathematical soundness of the approach. However, this is only part of the story because phase-field models do not need to have a moving-boundary problem associated and can be rigorously derived from classical thermomechanics. In this context, the distinguishing feature is that constitutive models depend on the variational derivative of the free energy. In all, phase-field models open the opportunity for the efficient treatment of outstanding problems in computational mechanics, such as, the interaction of a large number of cracks in three dimensions, cavitation, film and nucleate boiling, tumor growth or fully three-dimensional air-water flows with surface tension. In addition, phase-field models bring a new set of challenges for numerical discretization that will excite the computational mechanics community.

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“…Specifically, we consider a vapor bubble dynamics problem that was originally studied in [32,41]. In this example, two vapor bubbles of different radii are originally placed close to each other.…”

Section: Coalescence Of Two Bubbles In the Absence Of Gravitymentioning

confidence: 99%

Functional Entropy Variables: A New Methodology for Deriving Thermodynamically Consistent Algorithms for Complex Fluids, with Particular Reference to the Isothermal Navier-Stokes-Korteweg Equations

Liu¹,

Gómez²,

Evans³

et al. 2012

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. We propose a new methodology for the numerical solution of the isothermal Navier-Stokes-Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionally stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws. AbstractWe propose a new methodology for the numerical solution of the isothermal Navier-StokesKorteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionally stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws.

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The Second Gradient Method for the Direct Numerical Simulation of Liquid–Vapor Flows with Phase Change

Cited by 252 publications

References 31 publications

On stability condition for bifluid flows with surface tension: Application to microfluidics

On stability condition for bifluid flows with surface tension: Application to microfluidics

Computational Phase‐Field Modeling

Functional Entropy Variables: A New Methodology for Deriving Thermodynamically Consistent Algorithms for Complex Fluids, with Particular Reference to the Isothermal Navier-Stokes-Korteweg Equations

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