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Appl. Sci. 2017, 7(3), 277; doi:10.3390/app7030277

A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method

Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
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Author to whom correspondence should be addressed.
Academic Editor: Artur J. Jaworski
Received: 7 February 2017 / Revised: 5 March 2017 / Accepted: 9 March 2017 / Published: 11 March 2017
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Abstract

An unconditionally stable thermal lattice Boltzmann method (USTLBM) is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE) through Chapman–Enskog (C-E) expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM). Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes. View Full-Text
Keywords: lattice Boltzmann method; unconditionally stable; thermal flows; second-order of accuracy lattice Boltzmann method; unconditionally stable; thermal flows; second-order of accuracy
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Chen, Z.; Shu, C.; Tan, D.S. A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method. Appl. Sci. 2017, 7, 277.

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