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Paper: Reconstruction Method for M1 Equations of Radiative Transfer
Volume: 474, Numerical Modeling of Space Plasma Flows (ASTRONUM2012)
Page: 233
Authors: Hanawa, T.; Kanno, Y.; Harada, T.
Abstract: We propose a new method to construct numerical flux for the M1 equations of radiative transfer. The numerical flux is expressed as an explicit function of the energy density, E, and energy flux, F. It is constructed from the specific intensity distribution used to derive the closure relation. The flux has the upwind property in the sense that it gives a physical solution (cE >|F| > 0) as far as the CFL condition is satisfied. Here the symbol, c, denotes the speed of light. At the same time, it can solve passage of a flash successfully, i.e., the radiation energy diminishes quickly after the passage. This means the flux causes very limited numerical diffusion. The flux can be modified by taking account of absorption, emission, and scattering within a numerical cell. The modified flux reproduces the diffusion approximation when the numerical cell itself has a large optical depth. We show application to irradiated protoplanetary disks as well as several technical test problems.
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