Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations

. Many kinetic models of the Boltzmann equation have a diffusive scaling that leads to the Navier-Stokes type parabolic equations as the small scaling parameter approaches zero. In practical applications, it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter, from the rarefied kinetic regimes to the hydrodynamic diffusive regimes. An earlier approach in 11 reformulates such systems into the common hyperbolic relaxation system by Jin and Xin for hyperbolic conservation laws used to construct the relaxation schemes, and then use a multistep time splitting method to solve the relaxation system. Here we observe that the combination of the two time-split steps may yield a hyperbolic-parabolic systems that are more advantageous, in both stability and efficiency, for numerical computations. We show that such an approach yields a class of asymptotic-preserving (AP) schemes which are suitable for the computation of multiscale...