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.

Improvement of Two-Component Model of the Finite Difference Lattice Boltzmann Method for a Gas-Liquid Flow Simulation

2007 ◽  
Author(s):  
Shinsuke Tajiri ◽  
Michihisa Tsutahara ◽  
Long Wu
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Density Ratio ◽  
Flow Simulation ◽  
Surface Force ◽  
Large Density ◽  
Two Component ◽  
Large Density Ratio ◽  
Boltzmann Method

An Improved model of the finite difference lattice Boltzmann method which allows us to consider gas-liquid two component flows with a large density ratio like air-water flows was proposed. Simulations of the two component fluids which have a free interface and a large density ratio were demonstrated. The model which has compressibility of fluid and allows us to consider the pressure waves propagating in water like water hammers was presented. The basic idea is to decrease a density fluctuation by giving a large pressure gradient. The compressibility of liquid was controlled by choosing the bulk modulus. In order to simulate immiscible two fluids, the modulated diffusion scheme proposed by Latva-Kokko et al. was employed. The scheme is able to produce a smooth interface by allowing a certain amount of interface diffusion. The continuum surface force proposed by Brackbill et al. was employed as surface tension. A collapse of liquid column was calculated in order to confirm the relation between the inertia of liquid with a large density and the gravity, and the appropriate result was obtained.

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