<abstract xmlns="http://www.w3.org/1999/xhtml"> Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.</abstract>

Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.

A dynamically adaptive lattice Boltzmann method for thermal convection problems

Institute of Aerodynamics and Flow Technology German Aerospace Center (DLR), Bunsenstrasse 10, 37073 Göttingen, Germany

Institute of Thermodynamics and Fluid Mechanics University of Technology in Ilmenau, Helmholtzring 1, 98693 Ilmenau,

Aerodynamics and Flight Mechanics Research Group University of Southampton, Highfield Campus, Southampton SO17 1BJ,

United Kingdom of Great Britain and Northern Ireland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A dynamically adaptive lattice Boltzmann method for thermal convection problems"}

Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and...

A dynamically adaptive lattice Boltzmann method for thermal convection problems

Article Category: Individual Article Information

Online veröffentlicht: 30. Dez. 2016

Seitenbereich: 735 - 747

Eingereicht: 30. Sept. 2015

Akzeptiert: 08. Juni 2016

DOI: https://doi.org/10.1515/amcs-2016-0051

© by Ralf Deiterding

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.