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A univariate polynomial equation is presented. It provides models of thethermal lattice Boltzmann equation. The models can be accurate up to anyrequired level and can be applied to regular lattices, which allow efficientand accurate approximate solutions of the Boltzmann equation. We derive modelssatisfying the complete Galilean invariant and providing accuracy of the4th-order moment and beyond. We simulate thermal shock tube problems toillustrate the accuracy of our models and to show the remarkably enhancedstability obtained by our models and our discretized equilibrium distributions.

Univariate Polynomial Equation Providing Models of Thermal Lattice Boltzmann Theory