L -splines as diffusive limits of dissipative kinetic models

Gabriella Bretti (1) , Laurent Gosse (2) , Nicolas Vauchelet (3)

1 MeMoMat - Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
2 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
3 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Equations aux dérivées partielles [math.AP]

Gabriella Bretti, Laurent Gosse, Nicolas Vauchelet. L -splines as diffusive limits of dissipative kinetic models. Vietnam Journal of Mathematics, In press. ⟨hal-02440798⟩