Simulation of compressible two-phase flows with topology change of fluid–fluid interface by a robust cut-cell method

Lin, JianYu; Shen, Yi; Ding, Hang; Liu, Nansheng; Lu, Xi‐Yun

doi:10.1016/j.jcp.2016.10.023

Cited by 32 publications

(7 citation statements)

References 57 publications

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“…In addition, any cutcell method development must satisfy the consistency condition, whereby a solid body moving at the same relative velocity as the surrounding fluid should produce an exact solution. Published literature on cut-cell methods for moving boundary problems include cell merging [43,44] methods, implicit time-stepping [55,56] and flux redistribution methods [35,57], as well as recent developments by Muralidhran & Menon [52], Lin et al [58], Deng & li [59] and Patel & Lakdawala [60].…”

Section: Introductionmentioning

confidence: 99%

A moving boundary flux stabilization method for Cartesian cut-cell grids using directional operator splitting

Bennett

Nikiforakis

Klein

2018

Journal of Computational Physics

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An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A 367, no. 1907, 4559-4575 (2009, the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of "standard fluxes" from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Many diffuse immersed boundary methods used in recent literature employ artificial volume forces distributed over a zone of cells close to the interface to effectively represent the pressure force exerted by the immersed boundary. This stress can be distributed to the surrounding fluid using, for example, a dirac delta function, a distributed function or a forcing term. Early examples can be found in [4][5][6][7]. The advantage of this approach is that the wall geometry appears only in the distributed momentum forces, while the surface geometry does not otherwise affect the scheme. In particular, intersections of the wall geometry with computational cells do not have to be accounted for explicitly. Recent developments using this approach include particle flow applications [8,9] and heat transfer applications [10,11].Another popular class of diffuse boundary methods are the "fictitious domain" methods. In this approach, both fluid and solid regions are treated mathematically as a fluid, with either a material-dependent rigidity constraint, as in Glowinski et al. [12], or the fluid and solid regions are treated as a porous medium, using the Navier Stokes/Brinkmann equations with a permeability parameter-based forcing term, as in Angot et al. [13] and Khadra et al. [14]. Recent, notable developments to the fictitious domain approach include Randrianarivelo et al. [15], Angot [16]...

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Section: Introductionmentioning

confidence: 99%

A moving boundary flux stabilization method for Cartesian cut-cell grids using directional operator splitting

Bennett

Nikiforakis

Klein

2018

Journal of Computational Physics

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“…Following Ref. [17], we extend the interface velocity to the cells in the vicinity of the interface along the normal direction. In addition, the interfacial fluxes can be computed by…”

Section: The Four-wave Approximate Riemann Solvermentioning

confidence: 99%

“…In addition, in the diffuse interface methods, the interface profile tends to be thickened over time due to numerical diffusion. Although several interface sharpening schemes have been developed to suppress the interface diffusion [14][15][16], it remains a big challenge to conduct long-time simulations with the diffuse interface methods [17].…”

Section: Introductionmentioning

confidence: 99%

A fully conservative sharp-interface method for compressible mulitphase flows with phase change

Tian¹,

Cai²,

Pan³

2021

Preprint

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A fully conservative sharp-interface method is developed for multiphase flows with phase change. The coupling between two phases is implemented via introducing the interfacial fluxes, which are obtained by solving a general Riemann problem with phase change. A novel four-wave model is proposed to obtain an approximate Riemann solution, which simplifies the eightdimensional roo-finding procedure in the exact solver to a sole iteration of the mass flux. Unlike in the previous research, the jump conditions of all waves are imposed strictly in the present approximate Riemann solver so that conservation is guaranteed. Different choices of the fluid states used in the phase change model are compared, and we have shown that the adjacent

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“…23 The reconstructed discontinuous Galerkin (rDG) method 24 is computationally costly, and needs a positivity preserving limiter. The cut-cell method 25 with high interface resolution requires special treatment of the re-initialization of the level-set function. In the recent work in Reference 26, the curvature is computed using parabolic fitting of the interface; however, it requires low-Mach number corrections for a well-balanced scheme.…”

Section: Introductionmentioning

confidence: 99%

An ALE‐based finite element strategy for modeling compressible two‐phase flows

Potghan

Jog

2022

Numerical Methods in Fluids

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In this work, we develop a numerical strategy for solving two-phase immiscible compressible fluid flows in a general arbitrary Lagrangian-Eulerian framework.The interpolation functions for the field variables are chosen so as to produce a stable numerical formulation. We model one of the fluids in a Lagrangian setting and use a conforming mesh moving with it which circumvents the need of solving an additional diffusion equation to track or construct the interface. The discontinuity in the pressure field across the interface is accurately modeled using the dummy-node technique. This technique yields a sharp and accurate representation of the interface and in turn a correct computation of the surface tension forces. We present a variational form of the governing equations including the surface tension effect and their exact linearization. Various benchmark examples are presented to illustrate the good performance and good coarse-mesh accuracy of the proposed scheme.

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Simulation of compressible two-phase flows with topology change of fluid–fluid interface by a robust cut-cell method

Cited by 32 publications

References 57 publications

A moving boundary flux stabilization method for Cartesian cut-cell grids using directional operator splitting

A moving boundary flux stabilization method for Cartesian cut-cell grids using directional operator splitting

A fully conservative sharp-interface method for compressible mulitphase flows with phase change

An ALE‐based finite element strategy for modeling compressible two‐phase flows

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