Spectral Lagrangian methods for non-linear Boltzmann
type eqautions Irene Gamba,UT
Austin
Abstract:
We present a deterministic spectral solver for the non-linear Boltzmann
Transport Equation (energy conservative and non-conservative) for
rather general collision kernels. The computation of the non-linear
Boltzmann Collision integral and the lack of appropriate conservation
properties due to spectral methods has been taken care by framing the
conservation properties in the form of a constrained minimization
problem which is solved easily using a Lagrange multiplier method. We
benchmark our code with several examples of models for Maxwell type of
interactions, (elastic or inelastic) for which explicit solution
formulas are known. The numerical moments are compared with exact
moments formulas and the numerical non-equilibrium probability
distributions functions are compared to the general asymptotic results.
In the case of space inhomogeneous boundary value problems, the
numerical method captures the discoutinuous behahior of
the probability distribution functions solution of the BTE with
diffusive boundary conditions and sudden changes in boundary
temperature, as predicted by Y. Sone for solutions of the BTE and
computed by Aoki, et al .91, using alternative models.