scholarly journals Evaluation of the Single-Population Lattice Boltzmann Method for One-Dimensional Compressible Flows

2021 ◽  
Author(s):  
Samuel J. Mitchell ◽  
Sina Stapelfeldt ◽  
Ricardo Puente
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Single Population ◽  
One Dimensional ◽  
Boltzmann Method

scholarly journals Semi-Lagrangian lattice Boltzmann method for compressible flows

2020 ◽  
Vol 101 (5) ◽  
Author(s):  
Dominik Wilde ◽  
Andreas Krämer ◽  
Dirk Reith ◽  
Holger Foysi
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Boltzmann Method

A SIMPLE METHOD TO CONSTRUCT LOCAL EQUILIBRIUM FUNCTION FOR LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 24 (06) ◽  
pp. 1350038
Author(s):  
P. WANG ◽  
S. Q. ZHANG
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Local Equilibrium ◽  
New Method ◽  
Ratio Test ◽  
Simple Method ◽  
One Dimensional ◽  
Equilibrium Function ◽  
The One ◽  
Boltzmann Method

We have developed a simple method to construct local equilibrium function for lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one-dimensional Sod flow, one-dimensional Lax flow and thermal Couette flow are presented. Good results obtained using proposed new method, indicate that the proposed method is potentially capable of constructing of the local equilibrium function for LBM.

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.

scholarly journals A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiaojie Li ◽  
Zhoushun Zheng ◽  
Shuang Wang ◽  
Jiankang Liu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
One Dimensional ◽  
Explicit Finite Difference ◽  
Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

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