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Three-dimensional finite-difference lattice Boltzmann model and its application to inviscid compressible flows with shock waves
HE Yaling 1 *,LIU Qing 2 #,LI Qing 2
1.Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University,Xi’an 710049
2.Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University,Xi’an, Shaanxi, China, 710049
*Correspondence author
#Submitted by
Subject:
Funding: The Ph.D Programs Foundation of Ministry of Education of China （No.No. 20110201110038）
Opened online: 6 February 2013
Accepted by: none
Citation: HE Yaling,LIU Qing,LI Qing.Three-dimensional finite-difference lattice Boltzmann model and its application to inviscid compressible flows with shock waves[OL]. [ 6 February 2013] http://en.paper.edu.cn/en_releasepaper/content/4519464
 
 
In this paper, a three-dimensional (3D) finite-difference lattice Boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double-distribution-function approach. In the model, a density distribution function is adopted to model the flow field, while a total energy distribution function is adopted to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are derived from the Hermite expansions of the continuous equilibrium distribution functions. The discrete velocity set is obtained by choosing the abscissae of a suitable Gauss-Hermite quadrature with sufficient accuracy. In order to capture the shock waves in compressible flows and improve the numerical accuracy and stability, an implicit-explicit finite-difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations. The model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1D to 3D. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.
Keywords:compressible fluid dynamics; lattice Boltzmann model; Hermite expansion; finite-difference; shock wave; three-dimensional
 
 
 

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