Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Sofonea, Victor; Biciusca, Tonino; Busuioc, Sergiu; Ambruş, Victor E.; Gonnella, Giuseppe; Lamura, A.

doi:10.1103/physreve.97.023309

Cited by 22 publications

(15 citation statements)

References 113 publications

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“…With the discretisation of the velocity space, we also replace the Maxwell-Boltzmann equilibrium distribution with a set of distribution functions f eq k corresponding to the discrete velocity vectors v k . Due to the use of the vielbein formalism, the expression for f eq k coincides with the one employed on the flat Cartesian geometry [55] f eq…”

Section: The Vielbein Lattice Boltzmann Approachmentioning

confidence: 90%

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Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

et al. 2019

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We develop and implement a novel lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. Standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write down the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focussing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of a torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

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Section: The Vielbein Lattice Boltzmann Approachmentioning

confidence: 90%

“…in the Appendix of Ref. [55]. It is worth noting that, unlike standard lattice Boltzmann algorithm, in general the velocity directions do not coincide with the neighbouring lattice points.…”

Section: The Vielbein Lattice Boltzmann Approachmentioning

confidence: 99%

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

et al. 2019

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“…Due to the extraction of the heat through the lateral walls, the fluid temperature near the wall remains close to T w . Around the liquid-gas interface, where the fluid density is not constant, heat generation occurs due to the non-vanishing spurious velocity, which is known to plague multiphase simulations [12,32,68,69,70,71,72,73]. The stability and accuracy of our simulations is directly improved when the magnitude of these effects is reduced.…”

Section: Planar Interfacementioning

confidence: 99%

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Busuioc

Ambruş

Biciusca

et al. 2020

Computers & Mathematics with Applications

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We develop a two-dimensional Lattice Boltzmann model for liquid-vapour systems with variable temperature. Our model is based on a single particle distribution function expanded with respect to the full-range Hermite polynomials. In order to ensure the recovery of the hydrodynamic equations for thermal flows, we use a fourth order expansion together with a set of momentum vectors with 25 elements whose Cartesian projections are the roots of the Hermite polynomial of order Q = 5. Since these vectors are off-lattice, a fifth-order projection scheme is used to evolve the corresponding set of distribution functions. A fourth order scheme employing a 49 point stencil is used to compute the gradient operators in the force term that ensures the liquid-vapour phase separation and diffuse reflection boundary conditions are used on the walls. We demonstrate at least fourth order convergence with respect to the lattice spacing in the contexts of shear and longitudinal wave propagation through the van der Waals fluid. For the planar interface, fourth order convergence can be seen at small enough lattice spacings, while the effect of the spurious velocity on the temperature profile is found to be smaller than 1.0%, even when T w 0.7 T c . We further validate our scheme by considering the Laplace pressure test. Galilean invariance is shown to be preserved up to second order with respect to the background velocity. We further investigate the liquid-vapour phase separation between two parallel walls kept at a constant temperature T w smaller than the critical temperature T c and discuss the main features of this process.

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“…The classic torus shape of a collapsing cavitation bubble was successfully obtained. Very recently, Sofonea et al [69] successfully simulated bubble cavitation evolution in quiescent and sheared liquids using a third-order isothermal LBM coupled with van der Waals (vdW) equation of state.…”

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confidence: 99%

“…In reality, the density ratio can easily exceed 100 for a liquid-vapor twophase flow. Much effort has been expended to overcome the above-mentioned limitations [37][38][39]45,[50][51][52][53][54][55][56][59][60][61][64][65][66][67][68][69][70][71][72]. Yuan et al [37] redefined the effective mass function and managed to incorporate any real-gas EOS into LBM.…”

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confidence: 99%

Single-component multiphase lattice Boltzmann simulation of free bubble and crevice heterogeneous cavitation nucleation

Peng

Tian

et al. 2018

Phys. Rev. E

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This work serves as an important extension of previous work on cavitation simulation [Sukop and Or, Phys. Rev. E 71, 046703 (2005)10.1103/PhysRevE.71.046703]. A modified Shan-Chen single-component multiphase lattice Boltzmann method is used to simulate two different heterogeneous cavitation nucleation mechanisms, the free gas bubble model and the crevice nucleation model. Improvements include the use of a real-gas equation of state, a redefined effective mass function, and the exact difference method forcing scheme. As a result, much larger density ratios, better thermodynamic consistency, and improved numerical accuracy are achieved. In addition, the crevice nucleation model is numerically investigated using the lattice Boltzmann method. The simulations show excellent qualitative and quantitative agreement with the heterogeneous nucleation theories.

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Corner-transport-upwind lattice Boltzmann model for bubble cavitation

Cited by 22 publications

References 113 publications

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach

Two-dimensional off-lattice Boltzmann model for van der Waals fluids with variable temperature

Single-component multiphase lattice Boltzmann simulation of free bubble and crevice heterogeneous cavitation nucleation

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