Abstract
In this work, an asymptotic-preserving scheme is proposed for the electronic $M_1$ model in the diffusion limit. A very simple modification of the HLL numerical viscosity is considered in order to capture the correct asymptotic limit in the diffusion limit. This alteration also ensures the realizability of the numerical solution under a suitable CFL condition. Interestingly, it is proved that the new scheme can also be understood as a Godunov-type scheme based on a suitable approximate Riemann solver. Various numerical test cases are performed and the results are compared with a standard HLL scheme and an explicit discretization of the limit diffusion equation.
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