An asymptotic preserving method for transport equations with oscillatory scattering coefficients
It addresses the challenge of simulating multiscale transport problems for computational scientists working on kinetic equations.
The paper develops a numerical scheme for transport equations with oscillatory scattering coefficients that preserves both the diffusion limit and the homogenization limit, validated through numerical experiments.
We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures the homogenization limit as the length scale of the scattering coefficient goes to zero. The proposed method is based on the construction of multiscale finite element basis and a Galerkin projection based on the even-odd decomposition. The method is analyzed in the asymptotic regime, as well as validated numerically.