A Numerical Scheme for Quantum Boltzmann Equation Efficient in Fluid Regime
Friday, February 11, 1PM
Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [J. Comput. Phys., 229, 2010] to handle this kind of problems. The idea is to penalize the stiff collision term by a BGK type operator. This method, when applied to the quantum Boltzmann equation, is not practically effective due to the complexity of the quantum Maxwellians. The new contribution we make is to use a 'classical' BGK operator instead of the quantum one, and achieve a scheme that well captures the fluid limit and avoids computing the complicated Bose- Einstein or Fermi-Dirac distribution. A spectral method for the quantum collision operator is also discussed.
Host: S. Fomel and L. Ying