Discretization of the Boltzmann equation in velocity space using a Galerkin approach Original Research Article

A method for the discretization of the Boltzmann equation in velocity space via a Galerkin procedure with Hermite polynomials as trial and test functions is proposed. This procedure results in a set of partial differential equations, which is an alternative to the lattice-Boltzmann equations. These PDEs are discretized using an explicit finite difference scheme and a numerical example shows the validity of the approach.