An asymptotic preserving scheme for the M1 model on conical meshes
Xavier Blanc, Philippe Hoch, Clément Lasuen · HAL (Le Centre pour la Communication Scientifique Directe) · 2021
This work focuses on the design of a 2D numerical scheme for the M1 model on conical meshes. This model is nonlinear and approximates the firsts moments of the radiative transfert equation using an entropic closure. Besides, this model admits a diffusion limit as the cross section increases. It is important for the numerical scheme to be consistent with this limit, that is to say, it has to be asymptotic preserving or AP. Such a scheme already exists on polygonal meshes and our work consisted in adapting it to conical meshes. After having introduced conical meshes, we explain the construction of the scheme. It is based on an analogy between the M1 model and the Euler gas dynamic system. We also present a second order reconstruction procedure and we apply it on both polygonal and conical meshes. Moreover, we prove that the scheme converges toward a limit scheme in the diffusion limit. In the last section, some numerical test cases are given so as to compare the polygonal and conical schemes. The limit scheme is studied and we observed numerically that it is consistent with the diffusion equation. Eventually, the limit scheme is compared to a limit scheme coming from another moment model for the radiative transfer equation (namely, the P1 model).