LINEAR-STABILITY ANALYSIS OF THERMO-LATTICE BOLTZMANN MODELS

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