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We point out an equivalence between the discrete velocity method of solvingthe Boltzmann equation, of which the lattice Boltzmann equation method is aspecial example, and the approximations to the Boltzmann equation by a Hermitepolynomial expansion. Discretizing the Boltzmann equation with a BGK collisionterm at the velocities that correspond to the nodes of a Hermite quadrature isshown to be equivalent to truncating the Hermite expansion of the distributionfunction to the corresponding order. The truncated part of the distribution hasno contribution to the moments of low orders and is negligible at small Machnumbers. Higher order approximations to the Boltzmann equation can be achievedby using more velocities in the quadrature

Discretization of the Velocity Space in the Solution of the Boltzmann Equation