Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics

Abstract

In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis for the pure diffusive scaling case.

References in corpus (2)

• A convergent method for linear half-space kinetic equations
• A Hierarchy of Hybrid Numerical Methods for Multi-Scale Kinetic Equations

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• Asymptotic Analysis of Unsteady Neutron Transport Equation
• Random Sampling and Efficient Algorithms for Multiscale PDEs
• Generalized multiscale finite element method for the steady state linear Boltzmann equation
• On quantifying uncertainties for the linearized BGK kinetic equation