Implicit-explicit Finite-difference Lattice Boltzmann Method for Compressible Flows

Wang Yong; He Yaling; Tianshou Zhao; Guihua Tang; Wenquan Tao

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Implicit-explicit Finite-difference Lattice Boltzmann Method for Compressible Flows

Wang Yong 1 #,He Yaling 1 *,Tianshou Zhao 2,Guihua Tang 1,Wenquan Tao 1

1.State Key Laboratory of Multiphase Flow, School of Energy and Power Engineering, Xi’an Jiaotong University

2.Department of Mechanical Engineering, The Hong Kong University of Science and Technology

*Correspondence author

#Submitted by

Subject:

Funding: 国家自然科学基金,教育部重点项目,教育部博士点基金（No.50425620,306014,20050698036）

Opened online:24 December 2008

Accepted by: none

Citation: Wang Yong,He Yaling,Tianshou Zhao.Implicit-explicit Finite-difference Lattice Boltzmann Method for Compressible Flows[OL]. [24 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26916

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 the previous finite-difference and standard lattice Boltzmann methods. Numerical simulations of 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.

Keywords:Lattice Boltzmann method;implicit-explicit;finite-difference;compressible flows

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