In this work, we propose an asymptotic preserving scheme for a non-linear kinetic reaction-transport equation, in the regime of sharp interface. With a non-linear reaction term of KPP-type, a phenomenon of front propagation has been proved in [9]. This behavior can be highlighted by considering a suitable hyperbolic limit of the kinetic equation, using a Hopf-Cole transform. It has been proved in [6, 8, 11] that the logarithm of the distribution function then converges to the viscosity solution of a constrained Hamilton-Jacobi equation. The hyperbolic scaling and the Hopf-Cole transform make the kinetic equation stiff. Thus, the numerical resolution of the problem is challenging, since the standard numerical methods usually lead to high computational costs in these regimes. The Asymptotic Preserving (AP) schemes have been typically introduced to deal with this difficulty, since they are designed to be stable along the transition to the macroscopic regime. The scheme we propose is adapt 查看全文>>