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.

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.

A novel median dual finite volume lattice Boltzmann method for incompressible flows on unstructured grids

2020 ◽  
Vol 31 (12) ◽  
pp. 2050173
Author(s):  
Lei Xu ◽  
Wu Zhang ◽  
Zhengzheng Yan ◽  
Zheng Du ◽  
Rongliang Chen
Keyword(s):  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Unstructured Grids ◽  
Piecewise Linear ◽  
Distribution Functions ◽  
Order Scheme ◽  
Control Volumes ◽  
Boltzmann Method

A novel median dual finite volume lattice Boltzmann method (FV-LBM) for the accurate simulation of incompressible flows on unstructured grids is presented in this paper. The finite volume method is adopted to discretize the discrete velocity Boltzmann equation (DVBE) on median dual control volumes (CVs). In the previous studies on median dual FV-LBMs, the fluxes for each partial face have to be computed separately. In the present second-order scheme, we assume the particle distribution functions (PDFs) to be constant for all faces grouped around a particular edge. The fluxes are then evaluated using the low-diffusion Roe scheme at the midpoint of the edge, and the PDFs at the faces of the CV are obtained through piecewise linear reconstruction of the left and right states. The gradients of the PDFs are computed with the Green–Gauss approach. The presented scheme is validated on four benchmark flows: (a) pressure driven Poiseuille flow; (b) the backward-facing step flow with [Formula: see text], 100, 200 and 300; (c) the lid-driven flow with [Formula: see text] and 1000; and (d) the steady viscous flow past a circular cylinder with [Formula: see text], 20 and 40.

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.

ON BOUNDARY CONDITIONS IN THE FINITE VOLUME LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES

1999 ◽  
Vol 10 (06) ◽  
pp. 1003-1016 ◽  
Author(s):  
GONGWEN PENG ◽  
HAOWEN XI ◽  
SO-HSIANG CHOU
Keyword(s):  
Shear Flow ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Simple Shear ◽  
Lattice Boltzmann ◽  
Unstructured Meshes ◽  
Simple Shear Flow ◽  
Boltzmann Method

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

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