A finite-volume algorithm for modeling light transport with the time-independent simplified spherical harmonics approximation to the equation of radiative transfer

2011 ◽  
Author(s):  
Ludguier D. Montejo ◽  
Hyun-Keol K. Kim ◽  
Andreas H. Hielscher
Keyword(s):  
Radiative Transfer ◽  
Finite Volume ◽  
Spherical Harmonics ◽  
Light Transport ◽  
Volume Algorithm

scholarly journals A Finite-Volume Solution with a Bidirectional Upwind Difference Scheme for the Three-Dimensional Radiative Transfer Equation

2007 ◽  
Vol 64 (11) ◽  
pp. 4098-4112 ◽  
Author(s):  
Haruma Ishida ◽  
Shoji Asano
Keyword(s):  
Radiative Transfer ◽  
Difference Scheme ◽  
Finite Volume ◽  
Spherical Harmonic ◽  
Transfer Equation ◽  
Three Dimensional ◽  
Harmonic Series ◽  
Simultaneous Linear Equation ◽  
Upwind Difference Scheme ◽  
Cloud Models

Abstract A new calculation scheme is proposed for the explicitly discretized solution of the three-dimensional (3D) radiation transfer equation (RTE) for inhomogeneous atmospheres. To separate the independent variables involved in the 3D RTE approach, the spherical harmonic series expansion was used to discretize the terms, depending on the direction of the radiance, and the finite-volume method was applied to discretize the terms, depending on the spatial coordinates. A bidirectional upwind difference scheme, which is a specialized scheme for the discretization of the partial differential terms in the spherical harmonic-transformed RTE, was developed to make the equation determinate. The 3D RTE can be formulated as a simultaneous linear equation, which is expressed in the form of a vector–matrix equation with a sparse matrix. The successive overrelaxation method was applied to solve this equation. Radiative transfer calculations of the solar radiation in two-dimensional cloud models have shown that this method can properly simulate the radiation field in inhomogeneous clouds. A comparison of the results obtained using this method with those using the Monte Carlo method shows reasonable agreement for the upward flux, the total downward flux, and the intensities of radiance.

scholarly journals An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications

2018 ◽  
Vol 340 ◽  
pp. 684-727 ◽  
Author(s):  
Jibran Haider ◽  
Chun Hean Lee ◽  
Antonio J. Gil ◽  
Antonio Huerta ◽  
Javier Bonet
Keyword(s):  
Finite Volume ◽  
Volume Algorithm

scholarly journals A 3D short-characteristics method for continuum and line scattering problems in the winds of hot stars

2019 ◽  
Vol 633 ◽  
pp. A16 ◽  
Author(s):  
L. Hennicker ◽  
J. Puls ◽  
N. D. Kee ◽  
J. O. Sundqvist
Keyword(s):  
Radiative Transfer ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Resonance Line ◽  
Stellar Surface ◽  
Line Profiles ◽  
Hot Stars ◽  
Scattering Problems ◽  
Test Models ◽  
Volume Method

Context. Knowledge about hot, massive stars is usually inferred from quantitative spectroscopy. To analyse non-spherical phenomena, the existing 1D codes must be extended to higher dimensions, and corresponding tools need to be developed. Aims. We present a 3D radiative transfer code that is capable of calculating continuum and line scattering problems in the winds of hot stars. By considering spherically symmetric test models, we discuss potential error sources, and indicate advantages and disadvantages by comparing different solution methods. Further, we analyse the ultra-violet (UV) resonance line formation in the winds of rapidly rotating O stars. Methods. We consider both a (simplified) continuum model including scattering and thermal sources, and a UV resonance line transition approximated by a two-level-atom. We applied the short-characteristics (SC) method, using linear or monotonic Bézier interpolations, for which monotonicity is of prime importance, to solve the equation of radiative transfer on a non-uniform Cartesian grid. To calculate scattering dominated problems, our solution method is supplemented by an accelerated Λ-iteration scheme using newly developed non-local operators. Results. For the spherical test models, the mean relative error of the source function is on the 5 − 20% level, depending on the applied interpolation technique and the complexity of the considered model. All calculated line profiles are in excellent agreement with corresponding 1D solutions. Close to the stellar surface, the SC methods generally perform better than a 3D finite-volume-method; however, they display specific problems in searchlight-beam tests at larger distances from the star. The predicted line profiles from fast rotating stars show a distinct behaviour as a function of rotational speed and inclination. This behaviour is tightly coupled to the wind structure and the description of gravity darkening and stellar surface distortion. Conclusions. Our SC methods are ready to be used for quantitative analyses of UV resonance line profiles. When calculating optically thick continua, both SC methods give reliable results, in contrast to the alternative finite-volume method.

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