The M 1 radiative transfer model is considered in the present work in order to simulate the radiative fields and their interactions with the matter. The model is governed by an hyperbolic system of conservation laws supplemented by relaxation source terms. Several difficulties arise when approximating the solutions of the model; namely the positiveness of the energy, the flux limitation and and the limit diffusion behavior have to be satisfied. An HLLC scheme is exhibited and it is shown to satisfy all the required properties. A particular attention is payed concerning the approximate extreme waves. These approximations are crucial to obtain an accurate scheme. The extension to the full 2D problem is proposed. It satisfies, once again, all the expected properties. Numerical experiments are proposed. They show that the considered scheme is actually less diffusive than the currently used numerical methods.
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Berthon, C., Charrier, P. & Dubroca, B. An HLLC Scheme to Solve The M 1 Model of Radiative Transfer in Two Space Dimensions. J Sci Comput 31, 347–389 (2007). https://doi.org/10.1007/s10915-006-9108-6
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DOI: https://doi.org/10.1007/s10915-006-9108-6