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An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems

Part of: Basic methods in fluid mechanics Diffusion and convection

Published online by Cambridge University Press:  02 November 2016

Yang Hu ,
Decai Li ,
Shi Shu  and
Xiaodong Niu
Yang Hu*
Affiliation:
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China
Decai Li*
Affiliation:
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China
Shi Shu*
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, China
Xiaodong Niu*
Affiliation:
College of Engineering, Shantou University, Shantou, Guangdong, China
*
*Corresponding author. Email addresses:hy304@126.com (Y. Hu), dcli@bjtu.edu.cn (D. Li), shushi@xtu.edu.cn (S. Shu), xdniu@stu.edu.cn (X. Niu)
*Corresponding author. Email addresses:hy304@126.com (Y. Hu), dcli@bjtu.edu.cn (D. Li), shushi@xtu.edu.cn (S. Shu), xdniu@stu.edu.cn (X. Niu)
*Corresponding author. Email addresses:hy304@126.com (Y. Hu), dcli@bjtu.edu.cn (D. Li), shushi@xtu.edu.cn (S. Shu), xdniu@stu.edu.cn (X. Niu)
*Corresponding author. Email addresses:hy304@126.com (Y. Hu), dcli@bjtu.edu.cn (D. Li), shushi@xtu.edu.cn (S. Shu), xdniu@stu.edu.cn (X. Niu)
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Abstract

In this paper, a diffuse-interface immersed boundary method (IBM) is proposed to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin) in thermal flow problems. The novel IBM is implemented combining with the lattice Boltzmann method (LBM). The present algorithm enforces the three types of thermal boundary conditions at the boundary points. Concretely speaking, the IBM for the Dirichlet boundary condition is implemented using an iterative method, and its main feature is to accurately satisfy the given temperature on the boundary. The Neumann and Robin boundary conditions are implemented in IBM by distributing the jump of the heat flux on the boundary to surrounding Eulerian points, and the jump is obtained by applying the jump interface conditions in the normal and tangential directions. A simple analysis of the computational accuracy of IBM is developed. The analysis indicates that the Taylor-Green vortices problem which was used in many previous studies is not an appropriate accuracy test example. The capacity of the present thermal immersed boundary method is validated using four numerical experiments: (1) Natural convection in a cavity with a circular cylinder in the center; (2) Flows over a heated cylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentation of a single isothermal cold particle in a vertical channel. The numerical results show good agreements with the data in the previous literatures.

Keywords

Immersed boundary methodlattice Boltzmann methodthermal flowDirichlet boundary conditionNeumann boundary conditionRobin boundary conditionTaylor Green vortices

MSC classification

Secondary: 76M28: Particle methods and lattice-gas methods 76R05: Forced convection 76R10: Free convection
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 5 , November 2016 , pp. 1210 - 1257
Copyright
Copyright © Global-Science Press 2016 

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