Lattice Boltzmann thermohydrodynamics

Alexander, Francis J.; Chen, Shiyi; Sterling, James D.

doi:10.1103/physreve.47.r2249

Cited by 377 publications

(267 citation statements)

References 14 publications

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“…One may also define specular reflection conditions that yield a slip condition. Models for which energy is conserved allow specification of heat-transfer boundary conditions using particle reflection conditions as well [14]. These simple boundary conditions make the LB method particularly suited to parallel computing environments and the simulation of flows in complex geometries.…”

Section: The Lattice Boltzmann Discretizationmentioning

confidence: 99%

“…The inclusion of numerical viscosity is accomplished by Taylor expanding equation (26) about x and t. When the second order terms in this expansion are included in the above Chapman-Enskog analysis, the result is that the coefficient τ in the transport coefficients is simply replaced by τ − 1 2 (see reference [14]). Thus, the lattice contribution to the viscosity for this LB scheme is negative, requiring the value of the relaxation time to be greater than half of the time step to maintain positive viscosity.…”

Section: The Lattice Boltzmann Discretizationmentioning

confidence: 99%

“…This approach has much in common with explicit "penalty" or "pseudocompressibility" methods of solving incompressible flows [11] [12] [13]. Complete energy-conserving models that yield the correct form of the compressible continuity, momentum, and energy equations have been developed by Alexander, Chen, and Sterling [14] and by McNamara and Alder [15]. We note that for any of the LB models, the transport coefficients depend on the time step and lattice spacing.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Lattice Boltzmann Methods

Sterling

Chen

1996

Journal of Computational Physics

383

232

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The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it may be interpreted as a Lagrangian finite-difference method for the numerical simulation of the discrete-velocity Boltzmann equation that makes use of a BGK collision operator. As a result, it is not surprising that numerical instability of lattice Boltzmann methods have been frequently encountered by researchers. We present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constantdensity uniform mean flow. The linear stability depends on the following parameters: the distribution of the mass at a site between the different discrete speeds, the BGK relaxation time, the mean velocity, and the wavenumber of the perturbations. This parameter space is too large to compute the complete stability characteristics. We report some stability results for a subset of the parameter space for a 7-velocity hexagonal lattice, a 9-velocity square lattice and a 15-velocity cubic lattice. Results common to all three lattices are 1) the BGK relaxation time τ must be greater than 1 2 corresponding to positive shear viscosity, 2) there exists a maximum stable mean velocity for fixed values of the other parameters and 3) as τ is increased from 1 2 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger τ .

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Section: The Lattice Boltzmann Discretizationmentioning

confidence: 99%

Section: The Lattice Boltzmann Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of Lattice Boltzmann Methods

Sterling

Chen

1996

Journal of Computational Physics

383

232

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“…A number of authors have investigated rigorous LB methods where the energy balance is recovered as the higher-order velocity moments of the discrete species distribution functions (mass and momentum are conserved by considering the firstand second-order velocity moments) [21][22][23][24]. But progress in these methods has been limited especially for thermal two-phase flows due to the high computational demands and numerical instabilities.…”

Section: Introductionmentioning

confidence: 99%

Lattice-Boltzmann-based two-phase thermal model for simulating phase change

et al. 2013

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A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum limit one recovers the well known macroscopic energy conservation equation for the mixtures. Heats of reaction, the enthalpy change associated with the phase change, and the diffusive transport of enthalpy are all taken into account; but the dependence of enthalpy on pressure, which is usually a small effect in most nonisothermal flows encountered in chemical reaction systems, is ignored. The energy equation is coupled to the LB equations for species transport and pseudopotential interaction forces through the EOS by using the filtered local pseudotemperature field. The proposed scheme is validated against simple test problems for which analytical solutions can readily be obtained.

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“…In the last decade lattice kinetic theory, and most notably the Lattice Boltzmann method (see references [1] - [3]), have met with significant success for the numerical simulation of a large variety of athermal fluid flows, including realworld engineering applications. The simulation of flows with significant heat transfer turned out to be much more difficult (see reference [4], [5]).…”

Section: Introductionmentioning

confidence: 99%

Boundary Conditions for Thermal Lattice Boltzmann Simulations

D’Orazio

Succi

2003

Lecture Notes in Computer Science

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Abstract.A boundary condition for temperature and heat flux of a thermal lattice Boltzmann method is presented. A thermal lattice BGK model with doubled populations is used to simulate hydrodynamic and thermal fields for flows with viscous heating. The unknown thermal distribution functions at the boundary are assumed to be equilibrium distribution functions with a counter-slip internal energy density which is determined consistently with Dirichlet and/or Neumann boundary conditions.

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Lattice Boltzmann thermohydrodynamics

Abstract: We introduce a lattice Boltzmann computational scheme capable of modeling ther-

Cited by 377 publications

References 14 publications

Stability Analysis of Lattice Boltzmann Methods

Stability Analysis of Lattice Boltzmann Methods

Lattice-Boltzmann-based two-phase thermal model for simulating phase change

Boundary Conditions for Thermal Lattice Boltzmann Simulations

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