A Simple Second-Order Implicit-Explicit Asymptotic Preserving Scheme for the Hyperbolic Heat Equations

We propose an asymptotic preserving (AP) Implicit-Explicit (ImEx) scheme for the hyperbolic heat equation in the diffusive regime. This scheme is second order in time and space and l8-stabile under relatively low constraints on the time step, and without requiring the use slope limiters. The construction exploits a formalism developed in a previous work and, compared to it, leads to a simpler implementation but it loses uniform accuracy on paper. Stability and accuracy are verified on numerical examples, and even uniform accuracy is obtained on those. Finally, we discuss extensions of this method to the non linear case of isothermal Euler equations with friction.