Journal
PHYSICAL REVIEW E
Volume 83, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.83.046710
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We propose an approach to derive the thermal lattice Boltzmann method that is based on the Taylor expansion in variables of temperature as well as velocity and a direct calculation upon the Gaussian quadrature based hypothesis. This enables us to overcome the isothermal limitation and the low-order accuracy simultaneously. A systematic framework is explained for constructing numerically stable lattice Boltzmann models. The stability of this one-dimensional lattice Boltzmann model is demonstrated with a shock tube simulation.
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