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A Simplified Lattice Boltzmann Method without Evolution of Distribution Function

Part of: Rarefied gas flows, Boltzmann equation Basic methods in fluid mechanics

Published online by Cambridge University Press:  11 October 2016

Z. Chen ,
C. Shu ,
Y. Wang ,
L. M. Yang  and
D. Tan
Z. Chen
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260
C. Shu*
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260
Y. Wang
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260
L. M. Yang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing, Jiangsu 210016, China
D. Tan
Affiliation:
Department of Mechanical Engineering, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260
*
*Corresponding author. Email:mpeshuc@nus.edu.sg (C. Shu)
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Abstract

In this paper, a simplified lattice Boltzmann method (SLBM) without evolution of the distribution function is developed for simulating incompressible viscous flows. This method is developed from the application of fractional step technique to the macroscopic Navier-Stokes (N-S) equations recovered from lattice Boltzmann equation by using Chapman-Enskog expansion analysis. In SLBM, the equilibrium distribution function is calculated from the macroscopic variables, while the non-equilibrium distribution function is simply evaluated from the difference of two equilibrium distribution functions. Therefore, SLBM tracks the evolution of the macroscopic variables rather than the distribution function. As a result, lower virtual memories are required and physical boundary conditions could be directly implemented. Through numerical test at high Reynolds number, the method shows very nice performance in numerical stability. An accuracy test for the 2D Taylor-Green flow shows that SLBM has the second-order of accuracy in space. More benchmark tests, including the Couette flow, the Poiseuille flow as well as the 2D lid-driven cavity flow, are conducted to further validate the present method; and the simulation results are in good agreement with available data in literatures.

Keywords

Chapman-Enskog expansion analysislattice Boltzmann equationNavier-Stokes equationsmemory coststability

MSC classification

Secondary: 76M28: Particle methods and lattice-gas methods 76P99: None of the above, but in this section

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 1 - 22
Copyright
Copyright © Global-Science Press 2017 

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