Optimal relaxation collisions for lattice Boltzmann methods

Zhao, Fuzhang

doi:10.1016/j.camwa.2011.06.005

Cited by 30 publications

(8 citation statements)

References 13 publications

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“…The special case of τ 2 = 1/6 corresponds to the classic fourth order compact finite difference approximation for second order derivatives at grid points [30]. This value gives precisely the "optimal" collision time reported by Holdych et al [26] and is similar to that of Zhao [51], as found from a truncation error analysis of the lattice Boltzmann equation. The choice of τ 2 = 3/16 will eliminate the body force error while τ 2 = 1/4 eliminates the recurrence for T xx on the left hand side of equation (3.19).…”

Section: Momentssupporting

confidence: 63%

On the Lattice Boltzmann Deviatoric Stress: Analysis, Boundary Conditions, and Optimal Relaxation Times

Reis¹

2020

SIAM J. Sci. Comput.

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We analytically solve the two dimensional, nine-velocity, lattice Boltzmann model in planar channel flow and determine its deviatoric stress tensor. The shear component of its stress takes the expected Navier-Stokes form but the tangential component contains second order in Knudsen number contributions that one finds in solutions to the Burnett equations. Boundary conditions that neglect this Burnett contribution cause spurious grid-scale oscillations in the computed stress field within the computational domain. A moment-based boundary condition which considers the non-zero deviatoric stress is analysed and shown to completely eliminate the spurious oscillations seen in solutions using other boundary conditions. The analysis offers an explanation of previously reported optimal relaxation times in terms of the recurrence relation for the tangential stress and gives them an interpretation in terms of compact finite difference schemes.

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Section: Momentssupporting

confidence: 63%

On the Lattice Boltzmann Deviatoric Stress: Analysis, Boundary Conditions, and Optimal Relaxation Times

Reis¹

2020

SIAM J. Sci. Comput.

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“…As a result, smaller truncation errors can be achieved when relaxation times are less than 1.0. Therefore, in the BGK method, both relaxation times should be in the range (0.5-1] to obtain maximum stability and accuracy [22,24,51,[54][55][56]. According to Equations ( 13) and ( 14), at very high or very low Pr numbers, the relaxation time for either fluid flow or energy equation becomes τ ≈ 0.5 or τ 1.…”

Section: Methodsmentioning

confidence: 99%

A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Nabavizadeh

Barua

Eshraghi

et al. 2021

Fluids

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A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

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“…Because it has been proved by previous studies that the ideal value of τ g is around 1.0, which achieves optimal stability [36,37], the sub-operator equation L 1 is solved by the LBM solver for convection-diffusion equation and α o is chosen to be c 2…”

Section: Temperature Fieldmentioning

confidence: 99%

A fractional-step thermal lattice Boltzmann model for high Peclet number flow

Deng

Zhang

Wen

et al. 2015

Computers & Mathematics with Applications

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a b s t r a c tAs a promising approach in hydrodynamics and thermodynamics modeling, the lattice Boltzmann method (LBM) still suffers severe numerical instability when the temperature field of the flow is convection-dominant (high Peclet number). Despite a lot of research devoted to solve this problem worldwide, to simulate high Peclet number thermal flow at comparably few computational cost is still a hard work, making it inefficient in practical use. In this paper, we combine the LBM and the fractional-step method to propose a novel and stable thermal lattice Boltzmann scheme for high Peclet number flow without refining the lattice. By numerical tests of thermal Poiseuille flow and Couette flow, we quantify second-order accuracy of the proposed model, and through several cases of Peclet number from low to high, the superior stability and efficiency compared with existing thermal lattice Boltzmann model.

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Optimal relaxation collisions for lattice Boltzmann methods

Cited by 30 publications

References 13 publications

On the Lattice Boltzmann Deviatoric Stress: Analysis, Boundary Conditions, and Optimal Relaxation Times

On the Lattice Boltzmann Deviatoric Stress: Analysis, Boundary Conditions, and Optimal Relaxation Times

A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

A fractional-step thermal lattice Boltzmann model for high Peclet number flow

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