A NOVEL LESS DISSIPATION FINITE-DIFFERENCE LATTICE BOLTZMANN SCHEME FOR COMPRESSIBLE FLOWS

2012 ◽  
Vol 23 (11) ◽  
pp. 1250074 ◽  
Author(s):  
Q. CHEN ◽  
X. B. ZHANG
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Sufficient Conditions ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
Boltzmann Method ◽  
Lattice Boltzmann Scheme ◽  
Better Than ◽  
Good Agreement

In this paper, a new smoothness indicator is proposed to improve the finite-difference lattice Boltzmann method (FDLBM). The necessary and sufficient conditions for convergence are derived. A detailed analysis reveals that the convergence order is higher than that of the previous finite-difference scheme. The coupled double distribution function (DDF) model is used to describe discontinuity flows and verify the improvement. Numerical simulations of compressible flows with shock wave show that the improved finite-difference lattice Boltzmann scheme is accurate and has less dissipation. The numerical results are found to be in good agreement with the analytical results and better than those of the previous scheme.

Compressible Fluid Flow Simulation Using Finite Difference Lattice Boltzmann Method

2010 ◽  
Author(s):  
Vahid Abdollahi ◽  
Amir Nejat
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Contact Discontinuity ◽  
Flow Simulation ◽  
Viscous Flows ◽  
Pressure Shock ◽  
Boltzmann Method ◽  
Stationary Contact

A finite difference lattice Boltzmann method (FDLBM) is employed to simulate the compressible inviscid/viscous flows. The robustness of the employed approach is tested for the shock tube or Riemann problem in some distinct cases including strong pressure shock, the stationary contact discontinuity and the weak acoustic wave. The Results are compared with the exact solutions, as well as other classical finite volume CFD techniques (Steger-Warming, Roe and AUSM flux). The validity of the employed LBM approach is studied. This research reveals some of the challenges involved in simulating the compressible flows using FDLBM.

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.

Simulation of Flow over a Cavity Using Multi-Relaxation Time Thermal Lattice Boltzmann Method

2014 ◽  
Vol 554 ◽  
pp. 296-300 ◽  
Author(s):  
Nor Azwadi Che Sidik ◽  
Aman Ali Khan
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Flow Problem ◽  
Benchmark Solution ◽  
Flow Over A Cavity ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann ◽  
Lattice Boltzmann Scheme ◽  
Good Agreement

This article provides numerically study of the multi-relaxation time thermal lattice Boltzmann method (LBM) for compute the flow and isotherm characteristics in the bottom heated cavity located o n a floor of horizontal channel . A double-distribution function (DFF) was coupled with MRT thermal LBM to study the effects of various grashof number (Gr), Reynolds number (Re) and Aspect Ratio (AR) on the flow and isotherm characteristic. The results we re compared with the conventional single-relaxation time lattice Boltzmann scheme and benchmark solution for such flow configuration. The results of the numer ical simulation indicate that multi-relaxation time thermal lattice Boltzmann scheme demonstrated good agreement, which supports its validity in computing fluid flow problem.

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