Discontinuous spectral element method for solving radiative heat transfer in multidimensional semitransparent media

Zhao, Jingjun; Liu, L.H.

doi:10.1016/j.jqsrt.2007.02.001

Cited by 40 publications

(22 citation statements)

References 29 publications

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“…Comparison of simulated (a) radiative heat flux along the centerline of a sidewall (x ¼ À1.0, y ¼ 0, z) and (b) divergence of radiative heat flux along the centerline (x ¼ 0, y ¼ 0, z) for a 3-D rectangular enclosure containing absorbing, emitting, and nonscattering gas mixture at a specified temperature [Eq. (26)] with SNBCK gas model and different DG orders (P-1, P-2, and P-5), grid size (Dx ¼ Dy ¼ Dz), and angular quadratures (S 8 and T 4 ) with results reported in [40] (color figure available online).…”

Section: Resultsmentioning

confidence: 99%

“…The DG method provides enormous numerical flexibility and is distinguished by the following features: (1) It is elementwise conservative [23]; (2) it can provide arbitrarily high-order accuracy and polynomials [23]; (3) adaptive variants of the scheme can be developed, where n and mesh resolution may be refined locally [24,25]; (4) the method can be applied to general mesh topologies [26]; and (5) it is well suited for parallel computing using graphics processing units (GPUs). This last property results from the observation that the high-order DG uses dense local operators, an aspect that is further explained in [7].…”

Section: Discontinuous Galerkin Methods For Solving the Rtementioning

confidence: 99%

“…Zhao and Liu [26] developed the discontinuous spectral-element method combining the different orders (P-1 to P-14) of the DG method with the spectral-element method [28] to solve the 2-D RTE. In the spectral-element method, orthogonal polynomials such as Chebyshev and Legendre polynomials were used as the interpolation functions of a numerical solution to achieve high-order accuracy [26].…”

Section: Discontinuous Galerkin Methods For Solving the Rtementioning

confidence: 99%

“…In the spectral-element method, orthogonal polynomials such as Chebyshev and Legendre polynomials were used as the interpolation functions of a numerical solution to achieve high-order accuracy [26]. The authors calculated the radiative heat flux for an emitting, absorbing, and anisotropically scattering gray medium within a 2-D square enclosure with black walls.…”

Section: Discontinuous Galerkin Methods For Solving the Rtementioning

confidence: 99%

“…All previous studies using the DG method to solve the RTE considered black walls [23,26,29]. This section discusses the validity of our RTE solver for problems involving nonblack diffusive walls and diffusely emitting and reflecting boundaries.…”

Section: -D Radiative Transfer In Gray Emitting Absorbing and Nonmentioning

confidence: 99%

See 4 more Smart Citations

A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

Lee

Wilcox

et al. 2013

Numerical Heat Transfer, Part B: Fundamentals

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In this article we present a high-order-accurate solver for the radiative transfer equation (RTE) which uses the discontinuous Galerkin (DG) method and is designed for graphics processing units (GPUs). The compact nature of the high-order DG method enhances scalability, particularly on GPUs. High-order spatial accuracy can be used to reduce discretization errors on a given computational mesh, and can also reduce the mesh size needed to achieve a desired error tolerance. Computational efficiency is a key concern in solutions to radiative heat transfer problems, due to potentially large problem sizes created by (a) the presence of participating nongray media in a full-spectrum analysis, (b) the need to resolve a large number of angular directions and spatial extent of the domain for an accurate solution, and (c) potentially large variations in material and flow properties in the domain. We present here a simulation strategy, as well as a set of physical models, accompanied by a number of case studies, demonstrating the accuracy and superior performance in terms of computational efficiency of this approach.

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Section: Resultsmentioning

confidence: 99%

Section: Discontinuous Galerkin Methods For Solving the Rtementioning

confidence: 99%

Section: Discontinuous Galerkin Methods For Solving the Rtementioning

confidence: 99%

Section: Discontinuous Galerkin Methods For Solving the Rtementioning

confidence: 99%

Section: -D Radiative Transfer In Gray Emitting Absorbing and Nonmentioning

confidence: 99%

See 3 more Smart Citations

A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

Lee

Wilcox

et al. 2013

Numerical Heat Transfer, Part B: Fundamentals

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Opto‐Thermal Coupled Modeling

2024

Thermal Management for Opto‐electronics Packaging and Applications

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Recent progress in computational thermal radiative transfer

Tan

Zhao

et al. 2009

Chin. Sci. Bull.

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The equation describing the transfer of radiant energy in semitransparent media is radiative transfer equation. In three-dimensional semitransparent media, radiative intensity is a function of 7 dimensions, which can only be solved through the numerical method in most circumstances. Numerical simulation has become an important way in the study and application of the theory of thermal radiative transfer in semitransparent media. This paper reviews the recent progress of Chinese scholars in the field of computational thermal radiative transfer, and proposes some important subjects in this field for future study. thermal radiation, radiative transfer equation, computational methodFor theoretical study and engineering application of the theory of thermal radiative transfer in semitransparent media, the basic governing equation for the radiative energy transport process is radiative transfer equation (RTE). The RTE for a gray medium with uniform refractive index can be written as [in which r is the vector of spatial position; s is the vector of radiation direction; c 0 is speed of light in vacuum; n is the refractive index; I is the radiative intensity; I b is the black body emission intensity;  a is the absorption coefficient,  s is the scattering coefficient;  is scattering phase function; and t is time. The RTE describes the temporal, spatial and angular variation of the radiative intensity. The last term at the right hand side of eq. (1) includes an angular integration over the whole 4 solid angular space. As such, the radiative intensity of every direction is coupled together for scattering media, which demands for a coupled solution.The RTE is an integral-differential equation. Taking s as a velocity vector, ( , , )  I t s r s serves the role as a convection term, hence the RTE can be considered as a special kind of convection diffusion equation. Because radiative intensity is related to wavelength, time, spatial coordinates, and angular direction, which is a function of 7 variables in three-dimensional semitransparent media. Hence it is difficult to obtain analytical results and only numerical methods can be used in most cases. Nowadays, with the popularization of high performance computers, numerical simulation has become a very important tool for theoretical studies and engineering applications of the theory of thermal radiative transfer in semitransparent media. The already developed numerical methods in recent years for solving the RTE can be divided into two groups [3] : (1) methods based on ray tracing technique, and (2) methods based on global discretization of the differential form of the RTE. For the first group of methods, to trace the ray trajectory is essential to obtaining

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Discontinuous spectral element method for solving radiative heat transfer in multidimensional semitransparent media

Cited by 40 publications

References 29 publications

A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

A High-Order-Accurate GPU-Based Radiative Transfer Equation Solver for Combustion and Propulsion Applications

Opto‐Thermal Coupled Modeling

Recent progress in computational thermal radiative transfer

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