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. Numerical tests confirm these theoretical findings.