A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit

He, Xiaoyi; Chen, Shiyi; Doolen, Gary D.

doi:10.1006/jcph.1998.6057

Cited by 1,234 publications

(942 citation statements)

References 33 publications

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“…[29] Coupled transport of fluid flow, heat, and solute would not be possible to simulate accurately in the present model for molten titanium alloys, which is limited to a single grid spacing and time step, owing to the disparate rates of heat and solute transport. The thermal Lattice Boltzmann method for coupled heat and incompressible fluid flow fields has been used previously to simulate convection problems [29,[82][83][84] and been coupled to cellular automata (CA) to simulate the solidliquid phase change for pure materials. [7,31,32,36,79] If it is assumed that the fluid is incompressible, viscous heat dissipation is negligible, and no work is done by the external pressure, an additional set of distribution functions can be introduced to the model for heat transport.…”

Section: B the Lattice Boltzmann Methodsmentioning

confidence: 99%

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

Rolchigo

Mendoza

Samimi

et al. 2017

Metall Mater Trans A

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Additive manufacturing (AM) processes have many benefits for the fabrication of alloy parts, including the potential for greater microstructural control and targeted properties than traditional metallurgy processes. To accelerate utilization of this process to produce such parts, an effective computational modeling approach to identify the relationships between material and process parameters, microstructure, and part properties is essential. Development of such a model requires accounting for the many factors in play during this process, including laser absorption, material addition and melting, fluid flow, various modes of heat transport, and solidification. In this paper, we start with a more modest goal, to create a multiscale model for a specific AM process, Laser Engineered Net Shaping (LENS™), which couples a continuumlevel description of a simplified beam melting problem (coupling heat absorption, heat transport, and fluid flow) with a Lattice Boltzmann-cellular automata (LB-CA) microscale model of combined fluid flow, solute transport, and solidification. We apply this model to a binary Ti-5.5 wt pct W alloy and compare calculated quantities, such as dendrite arm spacing, with experimental results reported in a companion paper.

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Section: B the Lattice Boltzmann Methodsmentioning

confidence: 99%

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

Rolchigo

Mendoza

Samimi

et al. 2017

Metall Mater Trans A

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“…where f == f(x,~,t) is the single particle distribution function in the phase space (x,~), ~ the microscopic velocity, Tv the relaxation time, rtf the Maxwell-Boltzmann equilibrium distribution and F the external force term (15) where G is the external force per unit mass 40 and c the lattice speed for mass transfer defined as oj0/ with 0, representing the lattice constant (grid size) and 0/ the time step.…”

Section: Lattice Poisson-boltzmann Methodsmentioning

confidence: 99%

Electrokinetic Transport in Microchannels with Random Roughness

Wang

Kang

2009

Anal. Chem.

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I Email address: mwang(a),lanl.!!ov (M.W.); gkang@lanLgov (Q.K) Electrokinetic tr"t1'~n{',rt In microchannels Abstract: We present a numerical framework to model the electrokinetic transport in microchannels with random roughness. The three-dimensional microstructure of the rough channel is generated by a random generation-growth method with three statistical parameters to control the number density, the total volume fraction and anisotropy characteristics of roughness elements. The governing equations for the electrokinetic transport are solved by a high efficiency lattice Poisson-Boltzmann method in complex geometries. The effects from the geometric characteristics of roughness on the electrokinetic transport in microchannels are therefore modeled and analyzed. For a given total roughness volume fraction, a higher number density leads to a lower fluctuation due to the random factors. The electroosmotic permeability increases with the roughness number density nearly at a logarithmic law for a given volume fraction of roughness, but decreases with the volume fraction of roughness for a given roughness number density. When both the volume fraction and the number density of roughness are given, the electroosmotic permeability is enhanced by increases of the characteristic length along the external electric field direction or decreases of the length of the direction of across the channel.For a given microstructure of rough microchannel, the electroosmotic permeability decreases with the Debye length. Compared with the corresponding flows in a smooth channel, the rough surface may enhance the electrokinetic transport when the Debye length is smaller than the roughness characteristic height under the assumption of constant zeta potential for all surfaces.The present results may improve the understanding of the electrokinetic transport characteristics in microchannels.

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“…The price to pay is doubling of the storage requirements. The method has been successfully demonstrated for the case of Couette flow and Rayleigh-Benard convection (see reference [13]). The aim of this paper is to show that the doubled-LBE, with the new boundary conditions described in detail here, works over a pretty wide range of parameters and it can be extended so as to support velocity-pressure boundary conditions, which are of chief interest to practical engineering purposes.…”

Section: Introductionmentioning

confidence: 99%

“…This paper regards the double-species LBE model proposed in reference [13]. In this model the (thermal) energy is represented by a separate distribution function, g, which evolves concurrently with the standard particle distribution function f .…”

Section: The Thermal Lbe Modelmentioning

confidence: 99%

“…In [13], the bounce-back rule of the nonequilibrium distribution proposed by [15] is applied to the thermal population. In [16], the local thermal equilibrium distribution functions are applied on the wall nodes in the case of known temperature, while the energy distribution on the wall are set equal to those of the nearest interior nodes in the case of adiabatic wall.…”

Section: Boundary Conditionsmentioning

confidence: 99%

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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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A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit

Cited by 1,234 publications

References 33 publications

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

Electrokinetic Transport in Microchannels with Random Roughness

Boundary Conditions for Thermal Lattice Boltzmann Simulations

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