We present a flux-limiter approach adapted to asymptotic-preserving (AP) schemes developed for the hyperbolic heat equations (HHE). This method directly includes both the convective part of the system and the source term into the design of the slope limiters. It allows to fully benefit from the uniform accuracy of AP methods across all regimes as well as taking advantage of their enhanced stability properties. We also discuss the potential of the method for nonlinear applications and plasma applications.
Romain Duboscq, Ariane Trescases