A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

Zhao, Jingjun; Tan, Jun; Liu, L. H.

doi:10.1016/j.jcp.2012.08.020

Cited by 32 publications

(24 citation statements)

References 53 publications

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“…This confirms the equivalence of the LSFEM discretization with the LSORTE discretized by central difference scheme (as discussed in Section 3.1 and in Ref. [35]). …”

Section: E I S I     ωsupporting

confidence: 84%

“…To get further understanding of the LSFEM, here we show that the LSFEM discretization is equivalent to a central difference discretization of a kind of second order radiative transfer equation, which has just been proposed by the same author [35] and named as the least squares second order radiative transfer equation (LSORTE). By discretization with central difference like numerical method, such as the FEM and the meshless methods, the second order forms of radiative transfer equation shows better numerical properties than the RTE.…”

Section: Otherwisementioning

confidence: 99%

“…The error relations of the LSORTE discretized by central difference scheme [35] and the MSORTE discretized by central difference scheme [35] (4) The error distribution of the LSFEM is very similar to that of the LSORTE discretized by central difference scheme. This confirms the equivalence of the LSFEM discretization with the LSORTE discretized by central difference scheme (as discussed in Section 3.1 and in Ref.…”

Section: E I S I     ωmentioning

confidence: 99%

“…The This case was also studied in [35]. uniformly subdivided into 100 elements and the zenith angle is discretized using the Gauss integration with 20 discrete directions.…”

Section: Infinite Slab With An Inclusion Layermentioning

confidence: 99%

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A deficiency problem of the least squares finite element method for solving radiative transfer in strongly inhomogeneous media

Zhao

Tan

Liu

2012

Journal of Quantitative Spectroscopy and Radiative Transfer

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The accuracy and stability of the least squares finite element method (LSFEM) and the Galerkin finite element method (GFEM) for solving radiative transfer in homogeneous and inhomogeneous media are studied theoretically via a frequency domain technique. The theoretical result confirms the traditional understanding of the superior stability of the LSFEM as compared to the GFEM. However, it is demonstrated numerically and proved theoretically that the LSFEM will suffer a deficiency problem for solving radiative transfer in media with strong inhomogeneity. This deficiency problem of the LSFEM will cause a severe accuracy degradation, which compromises too much of the performance of the LSFEM and makes it not a good choice to solve radiative transfer in strongly inhomogeneous media. It is also theoretically proved that the LSFEM is equivalent to a second order form of radiative transfer equation discretized by the central difference scheme.

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“…This confirms the equivalence of the LSFEM discretization with the LSORTE discretized by central difference scheme (as discussed in Section 3.1 and in Ref. [35]). …”

Section: E I S I     ωsupporting

confidence: 84%

Section: Otherwisementioning

confidence: 99%

Section: E I S I     ωmentioning

confidence: 99%

“…The This case was also studied in [35]. uniformly subdivided into 100 elements and the zenith angle is discretized using the Gauss integration with 20 discrete directions.…”

Section: Infinite Slab With An Inclusion Layermentioning

confidence: 99%

See 2 more Smart Citations

A deficiency problem of the least squares finite element method for solving radiative transfer in strongly inhomogeneous media

Zhao

Tan

Liu

2012

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…In the application of DCM to solving the RTE, the moving least-squares (MLS) approximation is employed to construct the trial functions by using collocation points, and the DCM is adopted for constructing the linear equations as mentioned in Ref. 48.…”

Section: A Radiative Transfer Equationmentioning

confidence: 99%

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

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Radiative Transfer Equation and Solutions

Zhao¹,

Liu²

2018

Handbook of Thermal Science and Engineering

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A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

Cited by 32 publications

References 53 publications

A deficiency problem of the least squares finite element method for solving radiative transfer in strongly inhomogeneous media

A deficiency problem of the least squares finite element method for solving radiative transfer in strongly inhomogeneous media

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Radiative Transfer Equation and Solutions

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