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Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  14 September 2015

Yan Wang ,
Chang Shu ,
Chiang Juay Teo ,
Jie Wu  and
Liming Yang
Yan Wang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Chang Shu*
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Chiang Juay Teo
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Jie Wu
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Liming Yang
Affiliation:
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
*Corresponding author. Email addresses: [email protected] (Y. Wang), [email protected] (C. Shu), [email protected] (C. J. Teo), [email protected] (J. Wu), [email protected] (L.Yang)
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Abstract

A three-dimensional (3D) lattice Boltzmann flux solver (LBFS) is presented in this paper for the simulation of both isothermal and thermal flows. The present solver combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. It applies the finite volume method (FVM) to solve the N-S equations. Different from the conventional N-S solvers, its viscous and inviscid fluxes at the cell interface are evaluated simultaneously by local reconstruction of LBE solution. As compared to the conventional LBE solvers, which apply the lattice Boltzmann method (LBM) globally in the whole computational domain, it only applies LBM locally at each cell interface, and flow variables at cell centers are given from the solution of N-S equations. Since LBM is only applied locally in the 3D LBFS, the drawbacks of the conventional LBM, such as limitation to uniform mesh, tie-up of mesh spacing and time step, tedious implementation of boundary conditions, are completely removed. The accuracy, efficiency and stability of the proposed solver are examined in detail by simulating plane Poiseuille flow, lid-driven cavity flow and natural convection. Numerical results show that the LBFS has a second order of accuracy in space. The efficiency of the LBFS is lower than LBM on the same grids. However, the LBFS needs very less non-uniform grids to get grid-independence results and its efficiency can be greatly improved and even much higher than LBM. In addition, the LBFS is more stable and robust.

Keywords

Lattice Boltzmann flux solverlattice Boltzmann methodNavier-Stokes equationlid-driven cavity flowsnatural convection

MSC classification

Secondary: 76D05: Navier-Stokes equations
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 3 , September 2015 , pp. 593 - 620
Copyright
Copyright © Global-Science Press 2015 

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