A Novel Discrete Velocity Method for Solving the Boltzmann Equation Including Internal Energy and Non-Uniform Grids in Velocity Space

The discrete velocity method has been extended to include inelastic collisions with rotational-translational energy exchange. A single value of rotational energy per unit mass is assigned to every velocity in the velocity domain and inelastic collisions are modeled using the Larsen-Borgnakke method. The discrete velocity version of energy exchange is used to simulate both a homogeneous relaxation of a distribution with non-equilibrium rotational and translational temperatures and a 1D shock with rotational energy modes. The method has also been modified to allow for non-uniform grids in velocity space. Non-uniform grids permit computational effort to be focused on specific areas of interest within the velocity distribution function. The Bobylev-Krook-Wu solution to the Boltzmann equation (the only analytic solution known) is used to compare a non-uniform grid with a uniform grid.