A Central Difference Finite Volume Lattice Boltzmann Method for Simulation of 2D Inviscid Compressible Flows on Triangular Meshes

2018 ◽  
Author(s):  
Alireza Karbalaei ◽  
Kazem Hejranfar
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Lattice Boltzmann Equation ◽  
Triangular Meshes ◽  
Central Difference ◽  
Inviscid Compressible Flows ◽  
Boltzmann Method

In this work, a central difference finite volume lattice Boltzmann method (CDFV-LBM) is developed to compute 2D inviscid compressible flows on triangular meshes. The numerical solution procedure adopted here for solving the lattice Boltzmann equation is nearly the same as the procedure used by Jameson et al. for the solution of the Euler equations. The integral form of the lattice Boltzmann equation using the Gauss divergence theorem is applied on a triangular cell and the numerical fluxes on each edge of the cell are set to the average of their values at the two adjacent cells. Appropriate numerical dissipation terms are added to the discretized lattice Boltzmann equation to have a stable solution. The Boltzmann equation is discretized in time using the fourth-order Runge-Kutta scheme. The computations are performed for three problems, namely, the isentropic vortex and the supersonic flow around a NACA0012 airfoil and over a circular-arc bump. The effect of changing the grid resolution and the dissipation coefficients on the accuracy of the results is also studied. Results obtained by applying the CDFV-LBM are compared with the available numerical results which show good agreement.

DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS

2012 ◽  
Vol 19 ◽  
pp. 90-99
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
JINSHENG CAI
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
One Dimensional ◽  
Volume Method ◽  
Boltzmann Method ◽  
Boltzmann Model

In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

SIMULATION OF SHOCK-WAVE PROPAGATION WITH FINITE VOLUME LATTICE BOLTZMANN METHOD

2007 ◽  
Vol 18 (04) ◽  
pp. 447-454 ◽  
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
YONG TIAN CHEW
Keyword(s):  
Shock Wave ◽  
Wave Propagation ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Distribution Functions ◽  
Shock Wave Propagation ◽  
Simple Function ◽  
Boltzmann Method

A new approach was recently proposed to construct equilibrium distribution functions [Formula: see text] of the lattice Boltzmann method for simulation of compressible flows. In this approach, the Maxwellian function is replaced by a simple function which satisfies all needed relations to recover compressible Euler equations. With Lagrangian interpolation polynomials, the simple function is discretized onto a fixed velocity pattern to construct [Formula: see text]. In this paper, the finite volume method is combined with the new lattice Boltzmann models to simulate 1D and 2D shock-wave propagation. The numerical results agree well with available data in the literatures.

Symmetry Breaking of Flow in 2D Symmetric Channels: Simulations by Lattice-Boltzmann Method

1997 ◽  
Vol 08 (04) ◽  
pp. 859-867 ◽  
Author(s):  
Li-Shi Luo
Keyword(s):  
Boltzmann Equation ◽  
Symmetry Breaking ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Nonlinear Flow ◽  
Lattice Boltzmann Equation ◽  
Two Dimensional ◽  
Flow Phenomena ◽  
Boltzmann Method

In this paper, a numerical study of nonlinear flow phenomena in two-dimensional symmetric channels using the lattice-Boltzmann equation method is presented. The results are compared with both experimental results and other numerical results using some traditional methods. Comparisons are found to be quantitatively accurate.

A REVIEW OF THE LATTICE BOLTZMANN METHOD

1993 ◽  
Vol 04 (02) ◽  
pp. 409-415 ◽  
Author(s):  
S. SUCCI ◽  
R. BENZI ◽  
F. MASSAIOLI
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Porous Media ◽  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Equation ◽  
Boltzmann Method ◽  
Qualitative Discussion

In this paper, the basic elements of the theory of the Lattice Boltzmann equation are reviewed. Representative applications, such as turbulent flows and low-Reynolds flows in porous media are presented, along with a qualitative discussion on the most recent advances of this recent tool for computational fluid dynamics.

Parallel unstructured finite volume lattice Boltzmann method for high-speed viscid compressible flows

2021 ◽  
Author(s):  
Zhixiang Liu ◽  
Rongliang Chen ◽  
Lei Xu
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann Method ◽  
Parallel Algorithm ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Present Method ◽  
High Speed ◽  
Compressible Flows ◽  
Large Scale ◽  
Boltzmann Method

Based on the double distribution function Boltzmann-BGK equations, a cell-centered finite volume lattice Boltzmann method on unstructured grids for high-speed viscid compressible flows is presented. In the equations, the particle distribution function is introduced on the basis of the D2Q17 circular function, and its corresponding total energy distribution function is adopted. In the proposed method, the advective term is evaluated by Roe’s flux-difference splitting scheme, and a limiter is used to prevent the generation of oscillations. The distribution functions on the interface are calculated by piecewise linear reconstruction, in which the gradient is computed by the least-squares approach. In order to do large-scale simulations, a parallel algorithm is illustrated. The present method is validated by a flow around the NACA0012 airfoil and a flow past a circular cylinder at high Mach numbers. The results agree well with the published results, which demonstrate that the present method is an efficient numerical method for high-speed viscid compressible flows. The parallel performance results show that the proposed parallel algorithm achieves 90% parallel efficiency on 4800 cores for a problem with [Formula: see text] unstructured triangle cells, which shows the potential to perform fast and high-fidelity simulations of large-scale high-speed viscid compressible flows in complicated computational domains.

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