thesis, RWTH Aachen University (2012) ( ) Monreal, P.: Moment realizability and Kershaw closures in radiative transfer. Lewrence Livermore National Laboratory, Livermore (1976) Kershaw, D.S.: Flux Limiting Nature’s Own Way: A New Method for Numerical Solution of the Transport Equation, UCRL-78378. Garret, C.K., Hauck, C.D.: A comparison of moment closures for linear kinetic transport equations: the line source benchmark. Just, O., Obergaulinger, M., Janka, H.T.: A new multi-dimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics. 112, 2486–2506 (2011)īanach, Z., Larecki, W.: Spectral maximum entropy hydrodynamics of fermionic radiation: a three-moment system for one-dimensional flows. Larecki, W., Banach, Z.: Entropic derivation of the spectral Eddington factors. Method and code tests in spherical symmetry. Müller, B., Janka, H.T., Dimmelmeier, H.: A New multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. Rampp, M., Janka, H.T.: Radiation hydrodynamics with neutrinos-variable Eddington factor method for core-collapse supernova simulations. Smit, J.M., van den Horn, L.J., Bludman, S.A.: Closure in flux-limited neutrino diffusion and two-moment transport. Smit, J.M., Cernohorsky, J., Dullemond, C.P.: Hyperbolicity and critical points in two-moment approximate radiative transfer. 265, 345–354 (1992)Ĭernohorsky, J., Bludman, S.A.: Maximum entropy distribution and closure for Bose–Einstein and Fermi–Dirac radiation transport. Janka, H.T., Dgani, R., van den Horn, L.J.: Fermion angular distribution and maximum entropy Eddington factors. The fermionic Kershaw-type closure functions behave qualitatively in the same way as the fermionic maximum entropy closure functions, but attain different numerical values.Ĭernohorsky, J., van den Horn, L.J., Cooperstein, J.: Maximum entropy Eddington factors in flux-limited neutrino diffusion. It is proved that the obtained one-dimensional systems of transport equations are strictly hyperbolic and causal. The fermionic Kershaw-type closures differ from those previously derived for classical and bosonic radiation. The generalization of the former two-field case to three space dimensions is also presented. The second case includes additionally the flux of the heat flux as an independent variable. In the first case, the independent variables are the energy density and the heat flux. Next, the Kershaw-type two-field and three-field transport equations for fermionic radiation are analyzed. First, a description of the Kershaw-type closure for the system consisting of an arbitrary number of one-dimensional moment equations is presented. It is shown that the Kershaw-type closure procedure can also be applied to the spectral moment equations of fermionic radiation. In the case of classical and bosonic radiation, the closed-form analytic Kershaw-type and B-distribution closure procedures have been used. Besides the maximum entropy closure procedure, other procedures can be used to close the systems of spectral moment equations.
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