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For linear transport and radiative heat transfer equations with randominputs, we develop new generalized polynomial chaos based Asymptotic-Preservingstochastic Galerkin schemes that allow efficient computation for the problemsthat contain both uncertainties and multiple scales. Compared with previousmethods for these problems, our new method use the implicit-explicit (IMEX)time discretization to gain higher order accuracy, and by using a modifieddiffusion operator based penalty method, a more relaxed stability condition--ahyperbolic, rather than parabolic, CFL stability condition, is achieved in thecase of small mean free path in the diffusive regime. The stochasticAsymptotic-Preserving property of these methods will be shown asymptotically,and demonstrated numerically, along with computational cost comparison withprevious methods.

Efficient Stochastic Asymptotic-Preserving IMEX Methods for Transport Equations with Diffusive Scalings and Random Inputs