DG-IMEX stochastic Galerkin schemes for linear transport equation with random inputs and diffusive scalings
Kinetic theory connects the microscopic models with the macroscopic hydrodynamic models. The Knudsen number measures the ratio between the particle mean free path and a typical length scale. The equation becomes numerically stiff and requires expensive mesh sizes and time steps. To overcome this difficulty, it is known that asymptotic-preserving (AP) schemes can be designed to mimic the asymptotic transition from the kinetic equations to the hydrodynamic limit, in the discrete setting. For temporal and spatial discretizations, the explicit-implicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin is applied. A rigorous proof of the stochastic asymptotic-preserving (SAP) is given. The accuracy and SAP of the method are examined on the numerical experiments.
scientific article; zbMATH DE number 6826585
scientific article