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Thermal lattice Boltzmann method based on a theoretically simple derivation of the Taylor expansion
1Interdisciplinary Fusion Technology Division, KIST and University of Science and Technology, 136-791, Seoul, Republic of Korea. jae-wan.shim@polytechnique.org
Abstract:
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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