ℒ -Splines as Diffusive Limits of Dissipative Kinetic Models

Dissipative kinetic models inspired by neutron transport are studied in a (1 + 1)-dimensional context: first, in the two-stream approximation, then in the general case of continuous velocities. Both are known to relax, in the diffusive scaling, toward a damped heat equation. Accordingly, it is shown that “uniformly accurate” ℒ -splines discretizations of this parabolic asymptotic equation emerge from well-balanced schemes involving scattering S -matrices for the kinetic models. Moreover, well-balanced properties are shown to be preserved when applying IMEX time-integrators in the diffusive scaling. Numerical tests confirm these theoretical findings.