Thermal Lattice Boltzmann in Two Dimensions

Siebert, Diogo Nardelli; Hegele, Luiz A.; Surmas, Rodrigo; Santos, Luís Orlando Emerich dos; Philippi, Paulo C.

doi:10.1142/s0129183107010784

Cited by 26 publications

(35 citation statements)

References 6 publications

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“…, n b − 1, used to represent the microscopic velocity space. This formal relationship was found by Philippi and co-workers 29,30 and is based on the requirement that a discrete Hermitian representation respects the orthogonality described by Eq. (4) up to a given order, i.e.…”

Section: Projection Onto a Subspace: Finite Hermite Expansionmentioning

confidence: 91%

High-order regularization in lattice-Boltzmann equations

2017

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A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e. only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

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Section: Projection Onto a Subspace: Finite Hermite Expansionmentioning

confidence: 91%

High-order regularization in lattice-Boltzmann equations

2017

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“…Santos et al [38] applied the LB model to investigate the liquid junction potential at the interface between two electrolyte layers and the LB solutions were validated against the results of analytical and finite difference method for the evolution of concentration, net charge density and electrostatic potential. Santos et al have applied the LB model to more fields [39][40][41][42][43][44][45][46][47]. In summary, for the optimization of the design and the operating condition of microfluidic two-phase flow systems, the ability to predict flow patterns [22,23,48] and to simulate surface tension effects [49][50][51] is significant.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of immiscible liquid-liquid flow in microchannels using lattice Boltzmann method

et al. 2011

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Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators. The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet. The five distinct flow regimes of the kerosene-water system, previously identified in the experiments from Zhao et al., were reproduced. The quantitative and qualitative agreement between the simulations and the experimental data show the effectiveness of the numerical method. The roles of the interfacial tension and contact angle on the flow patterns and shapes of droplets were discussed and highlighted according to the numerical results based on the improved two-phase LB model. This work demonstrated that the developed LBM simulator is a viable tool to study immiscible two-phase flows in microchannels, and such a tool could provide tangible guidance for the design of various microfluidic devices that involve immiscible multi-phase flows.lattice Boltzmann method, immiscible two-phase flow, numerical simulation, microchannel, kerosene-water system

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“…Similar analysis (without the effect of the forcing) can be found in [40]. We start from the shifted equilibrium formulation…”

Section: Appendix Amentioning

confidence: 90%

“…The main added value with respect to previous similar calculations [40] is the explicit inclusion of the effects of the external force g in the Chapman-Enskog expansion. In order to perform the calculations, we need to introduce a hierarchy of temporal and spatial scales, via the introduction of a small parameter, ǫ:…”

Section: Thermal Kinetic Model and Continuum Theorymentioning

confidence: 99%

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Lattice Boltzmann methods for thermal flows: Continuum limit and applications to compressible Rayleigh–Taylor systems

Scagliarini¹,

Biferale²,

Sbragaglia

et al. 2010

Physics of Fluids

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We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible FourierNavier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-Bénard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ∼ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional RayleighTaylor systems with resolution up to Lx × Lz = 1664 × 4400 and with Rayleigh numbers up to Ra ∼ 2 × 10 10 .

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Thermal Lattice Boltzmann in Two Dimensions

Cited by 26 publications

References 6 publications

High-order regularization in lattice-Boltzmann equations

High-order regularization in lattice-Boltzmann equations

Numerical simulation of immiscible liquid-liquid flow in microchannels using lattice Boltzmann method

Lattice Boltzmann methods for thermal flows: Continuum limit and applications to compressible Rayleigh–Taylor systems

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