Parametric lattice Boltzmann method

Abstract The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete velocities as parameters. In addition, thermal flows are simulated by only five on-lattice discrete velocities and the distributions upon asymmetric sets of discrete velocities are introduced.