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Paper details
Number 4 - December 2016
Volume 26 - 2016
A dynamically adaptive lattice Boltzmann method for thermal convection problems
Kai Feldhusen, Ralf Deiterding, Claus Wagner
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.
Keywords
lattice Boltzmann method, adaptive mesh refinement, thermal convection, incompressible