Implicit-explicit finite-difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

2009 ◽  
Vol 59 (8) ◽  
pp. 853-872 ◽  
Author(s):  
Yong Wang ◽  
Yaling He ◽  
Jing Huang ◽  
Qing Li
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Explicit Finite Difference ◽  
Boltzmann Method ◽  
Oscillating Patterns

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.

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.

An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes

2017 ◽  
Vol 28 (04) ◽  
pp. 1750045 ◽  
Author(s):  
Ruofan Qiu ◽  
Rongqian Chen ◽  
Yancheng You
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Time Discretization ◽  
Good Convergence ◽  
Subgrid Model ◽  
Nonuniform Meshes ◽  
Runge Kutta ◽  
Explicit Finite Difference ◽  
Boltzmann Method

In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge–Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge–Kutta scheme and nonuniform meshes of present lattice Boltzmann method are discussed through simulations of a two-dimensional lid-driven cavity flow on nonuniform meshes. Moreover, the comparison simulations of the present method and multiple relaxation time lattice Boltzmann subgrid method are conducted qualitatively and quantitatively.

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