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A nonlinear moment model for radiative transfer equation. (English) Zbl 1472.78015

Summary: We derive a nonlinear moment model for the radiative transfer equation in three-dimensional (3D) space, using the method to derive the nonlinear moment model for the radiative transfer equation in slab geometry [Y. Fan et al., J. Comput. Phys. 404, Article ID 109128, 23 p. (2020; Zbl 1453.65248); SIAM J. Appl. Math. 80, No. 6, 2388–2419 (2020; Zbl 1455.35247)]. The resulting 3D \(HMP_N\) model enjoys a list of mathematical advantages, including global hyperbolicity, rotational invariance, physical wave speeds, and correct higher-order Eddington approximation. Simulation examples are presented to validate the new model numerically.

MSC:

78A35 Motion of charged particles
82C70 Transport processes in time-dependent statistical mechanics
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