http://image.sciencenet.cn/olddata/kexue.com.cn/upload/blog/file/2010/4/201049135149950926.pdf

Chebyshev collocation spectral method for one-dimensional radiative heat transfer in graded index media

Numerical smearing, ray effect, and angular false scattering in radiation transfer computation

This paper adopts the Runge–Kutta ray tracing method to obtain the ray-trajectory numerical solution in a two-dimensional gradient index medium. The emitting, absorbing and scattering processes are simulated by the Monte Carlo method. The temperature field and ray trajectory in the medium are obtained by the three methods, the Runge–Kutta ray tracing method, the ray tracing method with the cell model and the discrete curved ray tracing method with the linear refractive index cell model. Comparing the results of the three methods, it is found that the results by the Monte Carlo Runge–Kutta ray tracing method are of the highest accuracy. To improve the computational speed, the variable step-size Runge–Kutta ray tracing method is proposed, and the maximum relative error between the temperature field in the nonscattering medium by this method and the benchmark solution is less than 0.5%. The results also suggest that the Runge–Kutta ray tracing method would make the radiative transfer solution in the three-dimensional graded index media much easier.

Runge–Kutta ray tracing technique for solving radiative heat transfer in a two-dimensional graded-index medium

In general, the Stocks vector cannot be calculated in reverse in the vector radiative transfer. This paper presents a novel backward and forward Monte Carlo simulation strategy to study the vector radiative transfer in the participated medium. A backward Monte Carlo process is used to calculate the ray trajectory and the endpoint of the ray. The Stocks vector is carried out by a forward Monte Carlo process. A one-dimensional graded index semi-transparent medium was presented as the physical model and the thermal emission consideration of polarization was studied in the medium. The solution process to non-scattering, isotropic scattering, and the anisotropic scattering medium, respectively, is discussed. The influence of the optical thickness and albedo on the Stocks vector are studied. The results show that the U, V-components of the apparent Stocks vector are very small, but the Q-component of the apparent Stocks vector is relatively larger, which cannot be ignored.

https://iopscience.iop.org/article/10.3847/0004-637X/820/1/9/pdf

Backward and Forward Monte Carlo Method in Polarized Radiative Transfer

This paper develops a numerical model for thermal radiative transfer in a two-dimensional semitransparent graded index medium. A piecewise continuous refractive index model, the linear refractive index bar model, is presented. This model is established based on three hypotheses, and has a higher precision than the bar model used previously. This paper also studies the thermal emission from a two-dimensional graded index medium, which is scattering or non-scattering. We find that it can present an obvious pattern of directional distribution at times. The refractive index distribution and absorption coefficient are the two main influential factors. This finding differs from the common belief that thermal sources, such as the incandescent filament of a light bulb, emit a quasi-isotropic light. The finding also suggests that there maybe other important applications of artificial GRIN materials.

Thermal emission characteristics of a graded index semitransparent medium

This study develops numerical models for thermal emission in a two-dimensional semitransparent graded-index medium. Two piecewise continuous refractive index models, the bar model and the slab model, are presented. The formal is a combination of rectangular bars each having its own unique refractive index. The latter is a combination of slabs, each of which has a linear refractive index distribution. Two interface hypotheses are discussed: the reflection/refraction hypothesis and the refraction/total reflection hypothesis. The backward ray tracing method and the backward Monte Carlo method are employed for calculation. The apparent directional emissivity of a semitransparent medium with linear and nonlinear refractive index distributions is calculated. The results show that piecewise continuous refractive index can be used for modeling semitransparent media with continuously variable refractive index. Emission from the medium is complex and quite different from a medium with a constant refractive index, when the absorption coefficient is small and/or the refractive index varies greatly in the medium. The refractive/totally reflective inner interface in the bar model gives a more precise emission distribution and can be extended to simulate emission from a medium with a complex three-dimensional refractive index distribution.

Xin-Gang Liang

Papers

Approximate thermal emission models of a two-dimensional graded index semitransparent medium