Parametric schemes for the simulation of the advection process in finite-difference-based single-relaxation-time lattice Boltzmann methods

2020 ◽  
Vol 44 ◽  
pp. 101151
Author(s):  
Gerasim V. Krivovichev
Keyword(s):  
Relaxation Time ◽  
Finite Difference ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Methods ◽  
Single Relaxation Time

Simulation of Flow Past a Square Cylinder by Parallel Lattice Boltzmann Method using Multi-Relaxation-Time Scheme

2006 ◽  
Vol 22 (1) ◽  
pp. 35-42 ◽  
Author(s):  
J.-S. Wu ◽  
Y.-L. Shao
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Numerical Results ◽  
Channel Height ◽  
Blockage Ratio ◽  
Square Cylinder ◽  
Single Relaxation Time ◽  
Boltzmann Method

AbstractThe flows past a square cylinder in a channel are simulated using the multi-relaxation-time (MRT) model in the parallel lattice Boltzmann BGK method (LBGK). Reynolds numbers of the flow are in the range of 100 ∼ 1,850 with blockage ratio, 1/6, of cylinder height to channel height, in which the single-relaxation-time (SRT) scheme is not able to converge at higher Reynolds numbers. Computed results are compared with those obtained using the SRT scheme where it can converge. In addition, computed Strouhal numbers compare reasonably well with the numerical results of Davis (1984).

Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy’s flows

2016 ◽  
Vol 27 (04) ◽  
pp. 1650037 ◽  
Author(s):  
Pietro Prestininzi ◽  
Andrea Montessori ◽  
Michele La Rocca ◽  
Sauro Succi
Keyword(s):  
Porous Media ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Physical Dependence ◽  
Single Relaxation Time ◽  
Flows In Porous Media ◽  
Percent Accuracy ◽  
Boltzmann Method

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

IMPLICIT-EXPLICIT FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD FOR COMPRESSIBLE FLOWS

2007 ◽  
Vol 18 (12) ◽  
pp. 1961-1983 ◽  
Author(s):  
Y. WANG ◽  
Y. L. HE ◽  
T. S. ZHAO ◽  
G. H. TANG ◽  
W. Q. TAO
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Time Discretization ◽  
Taylor Vortex ◽  
Lattice Boltzmann Methods ◽  
Taylor Vortex Flow ◽  
Explicit Finite Difference ◽  
Boltzmann Method

We propose an implicit-explicit finite-difference lattice Boltzmann method for compressible flows in this work. The implicit-explicit Runge–Kutta scheme, which solves the relaxation term of the discrete velocity Boltzmann equation implicitly and other terms explicitly, is adopted for the time discretization. Owing to the characteristic of the collision invariants in the lattice Boltzmann method, the implicitness can be completely eliminated, and thus no iteration is needed in practice. In this fashion, problems (no matter stiff or not) can be integrated quickly with large Courant–Friedriche–Lewy numbers. As a result, with our implicit-explicit finite-difference scheme the computational convergence rate can be significantly improved compared with previous finite-difference and standard lattice Boltzmann methods. Numerical simulations of the Riemann problem, Taylor vortex flow, Couette flow, and oscillatory compressible flows with shock waves show that our implicit-explicit finite-difference lattice Boltzmann method is accurate and efficient. In addition, it is demonstrated that with the proposed scheme non-uniform meshes can also be implemented with ease.

Computation of coupled double-diffusive convection–radiation including lattice Boltzmann simulation of fluid flow

2013 ◽  
Vol 728 ◽  
pp. 146-162 ◽  
Author(s):  
F. Moufekkir ◽  
M. A. Moussaoui ◽  
A. Mezrhab ◽  
H. Naji
Keyword(s):  
Relaxation Time ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Lattice Boltzmann ◽  
Energy Equation ◽  
Double Diffusive Convection ◽  
Diffusive Convection ◽  
Multiple Relaxation Time ◽  
The Finite Difference Method ◽  
Double Diffusive

AbstractThis paper reports a numerical study of coupled double diffusive convection and radiation in a differentially heated square enclosure filled with non-grey air–CO2 (or air–H2O) mixtures. The numerical procedure is based on a hybrid scheme with the multiple relaxation time lattice Boltzmann method and the finite difference method. The fluid velocity is determined by the D2Q9 multiple relaxation time model, and the energy equation is discretized by the finite difference method to compute the temperature field, while the radiative part of the energy equation is calculated by the discrete ordinates method combined with the spectral line-based weighted sum of grey gases model. Depending on the boundary conditions, aiding and opposing flows occur as the result of temperature and concentration gradients. The effects of various parameters, such as the molar fraction on the flow structure, thermal and concentration fields, are investigated for aiding and opposing cases. The numerical results show that, in the presence of non-grey radiation, the heat transfer is decreased and the mass transfer is slightly modified. The gas radiation modifies the structure of the velocity and thermal fields by generating inclined stratifications and promoting instabilities in opposing flows.

scholarly journals On the moment system and a flexible Prandtl number

2014 ◽  
Vol 28 (06) ◽  
pp. 1450048 ◽  
Author(s):  
Raúl Machado
Keyword(s):  
Relaxation Time ◽  
Boltzmann Equation ◽  
Prandtl Number ◽  
Lattice Boltzmann ◽  
Continuous Distribution ◽  
Lattice Boltzmann Equation ◽  
Collision Model ◽  
Single Relaxation Time ◽  
Moment System ◽  
The Moment

The Maxwell–Boltzmann moment system can be seen as a particular case of a mathematically more general moment system proposed by Machado.1 These last moments, of which a suggested continuous distribution and an integral generating form are presented here for some orders, are used in this paper to theoretically show (one of) their usefulness: A flexible Prandtl number can be obtained in both the Boltzmann equation and in the lattice Boltzmann equation with a conventional single relaxation time Bhatnagar–Gross–Krook (BGK) collision model.

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