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Approximating the \(M_2\) method by the extended quadrature method of moments for radiative transfer in slab geometry. (English) Zbl 1333.78018

Summary: We consider the simplest member of the hierarchy of the extended quadrature method of moments (EQMOM), which gives equations for the zeroth-, first-, and second-order moments of the energy density of photons in the radiative transfer equations in slab geometry. First we show that the equations are well-defined for all moment vectors consistent with a nonnegative underlying distribution, and that the reconstruction is explicit and therefore computationally inexpensive. Second, we show that the resulting moment equations are hyperbolic. These two properties make this moment method quite similar to the attractive but far more expensive \(M_2\) method. We confirm through numerical solutions to several benchmark problems that the methods give qualitatively similar results.

MSC:

78M05 Method of moments applied to problems in optics and electromagnetic theory
82C70 Transport processes in time-dependent statistical mechanics

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References:

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