An energy-preserving level set method for multiphase flows

Valle, Nicolás; Trias, F. X.; González, Jesús Castro

doi:10.1016/j.jcp.2019.108991

Cited by 17 publications

(32 citation statements)

References 51 publications

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“…While we succeeded at the formulation of a fully mass conservative and energy-preserving scheme, the conservation of linear momentum is still unclear [16]. However, as it was already commented in [1], while the lack of total momentum conservation is an undesired property, the adoption of an energypreserving scheme provides a bound on total energy and thus stability. Nonetheless, the conservation of linear momentum is an active line of research that deserves further discussion.…”

Section: Discussionmentioning

confidence: 80%

“…We proceed as in [1] by discretizing differential geometry operators from a geometrical perspective and then construct discrete vector calculus operators within a finite volume method. Once we obtain the discrete versions of the differential geometry operators, we construct the discrete counterparts of divergence (D), gradient (G), Laplacian (L) and convective (C(•)) operators, resulting in a classical finite volume, second order, staggered method as introduced by Harlow and Welch [23,13].…”

Section: Discretizationmentioning

confidence: 99%

“…We then introduce the definition C(u f ) = DUΨ introduced in [24,1], where Ψ contains the high resolution cell-to-face interpolation, to yield…”

Section: Conservation Of Energymentioning

confidence: 99%

“…Regarding the inclusion of surface tension, Fuster [14] developed on top of a Volume Of Fluid (VOF) method a discretization focusing on preserving the (skew-)symmetry of the operators involved, albeit overlooked surface tension, which is know to introduce spurious oscillations that may eventually lead to the divergence of the numerical simulation [15]. In the context of the level set method, our previous work resulted in the inclusion of curvature in an energy-preserving fashion [1], while the conservation of momentum is still elusive, a well known issue for diffuse interface models [16]. Within phase-field methods, the pioneering work of Jacqmin [17] included surface tension in a consistent way in the context of the Cahn-Hilliard equation.…”

Section: Introductionmentioning

confidence: 99%

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Energy Preserving Multiphase Flows: Application to Falling Films

Valle¹,

Trias²,

Castro³

2021

14th WCCM-ECCOMAS Congress

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The numerical simulation of multiphase flows presents several challenges, namely the transport of different phases within de domain and the inclusion of capillary effects. Here, these are approached by enforcing a discrete physics-compatible solution. Extending our previous work on the discretization of surface tension [N. Valle, F. X. Trias, and J. Castro, "An energy-preserving level set method for multiphase flows," J. Comput. Phys., vol. 400, p. 108991, 2020] with a consistent mass and momentum transfer a fully energy-preserving multiphase flow method is presented. This numerical technique is showcased within the simulation of a falling film under several working conditions related to the normal operation of LiBr absorption chillers.

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Section: Discussionmentioning

confidence: 80%

Section: Discretizationmentioning

confidence: 99%

“…We then introduce the definition C(u f ) = DUΨ introduced in [24,1], where Ψ contains the high resolution cell-to-face interpolation, to yield…”

Section: Conservation Of Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Energy Preserving Multiphase Flows: Application to Falling Films

Valle¹,

Trias²,

Castro³

2021

14th WCCM-ECCOMAS Congress

Self Cite

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“…Let's assume that we use the same staggered formulation in conjunction with a second-order Adams-Bashforth scheme that, for the single phase case, led to the LU decomposition given in Eq.(10). However, for incompressible multiphase flows with interface tracking, density is not constant [15]. This necessarily leads to a modification of the block system of equations.…”

Section: Pressure-velocity Coupling: a Unified Frameworkmentioning

confidence: 99%

Symmetry-Preserving Discretization of Navier-Stokes on Unstructured Grids: Collocated Vs Staggered

Trias¹,

Valle²,

Gorobets³

et al. 2021

14th WCCM-ECCOMAS Congress

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The essence of turbulence are the smallest scales of motion. They result from a subtle balance between convective transport and diffusive dissipation. Mathematically, these terms are governed by two differential operators differing in symmetry: the convective operator is skew-symmetric, whereas the diffusive is symmetric and positive-definite. On the other hand, accuracy and stability need to be reconciled for numerical simulations of turbulent flows around complex configurations. With this in mind, a fully-conservative discretization method for general unstructured grids was proposed [Trias et al., J.Comp.Phys. 258, 246-267, 2014]: it exactly preserves the symmetries of the underlying differential operators on a collocated mesh. However, any pressure-correction method on collocated grids suffer from the same drawbacks: the cell-centered velocity field is not exactly incompressible and some artificial dissipation is inevitable introduced. On the other hand, for staggered velocity fields, the projection onto a divergence-free space is a well-posed problem: given a velocity field, it can be uniquely decomposed into a solenoidal vector and the gradient of a scalar (pressure) field. This can be easily done without introducing any dissipation as it should be from a physical point-of-view. In this work, we explore the possibility to build up staggered formulations based on collocated discrete operators.

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Conservation of energy in the direct numerical simulation of interface-resolved multiphase flows

Valle

Verstappen

2023

Exp. Comput. Multiph. Flow

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In the context of deformable bubbles, surface tension produces a dynamic exchange between kinetic and surface elastic energy. This exchange of energy is relevant to bubble dynamics, like bubble induced turbulence or drag reduction. Unfortunately, the underlying physical mechanism is not exactly explained by the state-of-the-art numerical methods. In particular, the numerical violation of energy conservation results in an uncontrolled evolution of the system and yields well-known numerical pathologies. To remedy these problems, we tackle two of the most problematic terms in the numerical formulation: convection and surface tension. We identify the key mathematical identities that imply both physical conservation and numerical stability, present a semi-discretization of the problem that is fully energy preserving, and assess their stability in terms of the discrete energy contributions. Numerical experiments showcase the stability of the method and its energy evolution for stagnant and oscillating inviscid bubbles. Results show robust as well as bounded dynamics of the system, representing the expected physical mechanism.

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An energy-preserving level set method for multiphase flows

Cited by 17 publications

References 51 publications

Energy Preserving Multiphase Flows: Application to Falling Films

Energy Preserving Multiphase Flows: Application to Falling Films

Symmetry-Preserving Discretization of Navier-Stokes on Unstructured Grids: Collocated Vs Staggered

Conservation of energy in the direct numerical simulation of interface-resolved multiphase flows

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