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Title: COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR schememore » can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.« less
Authors:
;  [1]
  1. Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
Publication Date:
OSTI Identifier:
22519960
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 223; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; APPROXIMATIONS; ASTROPHYSICS; COMPARATIVE EVALUATIONS; DIFFUSION; HYDRODYNAMICS; NONLINEAR PROBLEMS; RADIANT HEAT TRANSFER; RADIATION PRESSURE; RELAXATION; WAVE PROPAGATION