Transient radiative transfer in semi-transparent slab with arbitrary refractive index and collimated irradiation

Dehghanian, A.; Sarvari, S. M. Hosseini

doi:10.1016/j.icheatmasstransfer.2020.104731

Cited by 11 publications

(2 citation statements)

References 32 publications

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“…A low-rank approximation for time-dependent radiation transport in one-and two-dimensional Cartesian geometries has been discussed in [47]. In [15], a variable discrete ordinates method has been used to solve the transient radiation heat transfer in a semi-transparent slab. A Galerkin framework using even and odd parts of the solution in different finite-dimensional spaces for time time-dependent RTE is considered in [18].…”

Section: Model Problemmentioning

confidence: 99%

Operator-splitting finite element method for solving the radiative transfer equation

Ganesan,

Singh

2024

Numer Algor

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An operator-splitting finite element scheme for the time-dependent radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite element method are used for the spatial-angular discretization of the radiative transfer equation, whereas the backward Euler scheme is used for temporal discretization. Error analysis of the proposed numerical scheme for the fully discrete radiative transfer equation is presented. The stability and convergence estimates for the fully discrete problem are derived. Moreover, an operator-splitting algorithm for the numerical simulation of high-dimensional equations is also presented. The validity of the derived estimates and implementation is illustrated with suitable numerical experiments.

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Section: Model Problemmentioning

confidence: 99%

Operator-splitting finite element method for solving the radiative transfer equation

Ganesan,

Singh

2024

Numer Algor

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“…A low-rank approximation for time-dependent radiation transport in one-and two-dimensional Cartesian geometries has been discussed in [26]. In [9], a variable discrete ordinates method has been used to solve the transient radiation heat transfer in a semi-transparent slab. Despite several numerical schemes proposed in the literature, numerical solution of the time-dependent high-dimensional RTE is still challenging and is an active research field.…”

Section: Model Problemmentioning

confidence: 99%

An Operator-Splitting Finite Element Method for the Numerical Solution of Radiative Transfer Equation

Ganesan¹,

Singh²

2021

Preprint

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An operator-splitting finite element scheme for the time-dependent, highdimensional radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite element method are used for the spatial-angular discretization of the radiative transfer equation, whereas the implicit backward Euler scheme is used for temporal discretization. Error analysis of the proposed numerical scheme for the fully discrete radiative transfer equation is presented. The stability and convergence estimates for the fully discrete problem are derived. Moreover, an operator-splitting algorithm for numerical simulation of high-dimensional equations is also presented. The validation of the derived estimates and implementation is demonstrated with appropriate numerical experiments. KeywordsRadiative transfer equation • Operator-splitting method • Streamline upwind Petrov Galerkin finite element methods • Backward Euler scheme • Stability and Convergence analysis Mathematics Subject Classification (2010) MSC 65M12 • 65M15 • 65M60 • 65R20 1 IntroductionRadiation plays a significant role, both as a detectable and as a dominant mechanism for transmitting energy inside and outside a system, in several areas, including optics,

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Reconstruction of Absorption and Scattering Coefficients in a One-Dimensional Parallel Plane Variable Index Media

Dehghanian

Sarvari

2022

Iran J Sci Technol Trans Mech Eng

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Transient radiative transfer in semi-transparent slab with arbitrary refractive index and collimated irradiation

Cited by 11 publications

References 32 publications

Operator-splitting finite element method for solving the radiative transfer equation

Operator-splitting finite element method for solving the radiative transfer equation

An Operator-Splitting Finite Element Method for the Numerical Solution of Radiative Transfer Equation

Reconstruction of Absorption and Scattering Coefficients in a One-Dimensional Parallel Plane Variable Index Media

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