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Multispeed thermal models of the lattice Boltzmann method (LBM) that have a single relaxation [Bhatnagar-Gross-Krook (BGK)] scheme have been proposed by several authors. While these models are intended to correctly represent heat characteristics and compressibility, most of them do not provide satisfactory accuracy. This paper discusses how to construct a correct model. Thermally correct two-dimensional and three-dimensional multispeed LBM BGK models are proposed. The models are verified by simulations of Couette flow, evolution from circularly distributed temperature, and normal shock wave. The results show exact agreement with the theoretical predictions. The numerical stability of the model is demonstrated by the simulation of recovery from a random fluctuation.
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Watari et al. (2004) studied this question.
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