F08-3 Analysis of compressible flows by the lattice Boltzmann method

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.

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

Volume 7: Fluids Engineering ◽

10.1115/imece2018-86302 ◽

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.

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

International Journal of Modern Physics C ◽

10.1142/s0129183107011868 ◽

2007 ◽

Vol 18 (12) ◽

pp. 1961-1983 ◽

Cited By ~ 49

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.

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