Linear stability analysis of thermo-lattice Boltzmann models

The numerical stability of thermo-lattice Boltzmann (TLBE) models is presented. The TLBE algorithm is linearized and represented in matrix form. The spectral radius of the resulting matrix is obtained by the method of powers. In particular, the numerical stability of two 2-speed 13-bit TLBE models-one based on the hexagonal lattice, and the other on a square lattice-is examined. For these two TLBE models, as a function of the energy density, the achievable Reynolds number (before the onset of grid modes) is more than an order of magnitude greater for the hexagonal grid than for the square grid. (C) 1998 Academic Press.