Numerical Research On The Radiative Transfer In Participant Media By Natural Element Method

The propagation of the radiative light beams in the semitransparent participant media is described by radiative transfer equation. The forms of the radiative transfer equation vary with different applied fields, specifically including steady or transient scalar radiative transfer equation, and steady or transient vector radiative transfer equation. Many numerical methods based on discretization of the differential form of radiative transfer equation have been proposed. Different methods have their own advantages and application situations. People always keep on finding an efficient, fast numerical method for the radiative transfer problems, which is also convenient to be combined with other physical processes, such as fluid flow and combustion etc. Natural element method (NEM) is a kind of meshless method based on natural neighbor interpolation, and the shape function constructed by the natural neighbor interpolation has interpolation property, which makes it easily to impose the essential boundary condition. Thus, since the NEM has the advantages of both the meshless method and finite element method, and also overcomes the disadvantages of these two method, the NEM is a kind of promising numerical method for solving the partial differential equation. In this thesis, the NEM is applied to the numerical simulation of the thermal radiation. The natural element meshless method approach for steady or transient scalar radiative transfer equation, and steady or transient vector radiative transfer equation are established. The research on scalar and vector radiative transfer in optical complex inhomogeneous semitransparent participant media is conducted systematically.In NEM, the function space is approximated by the natural neighbor interpolation, including Sibson and Laplace interpolation. By using the natural neighbor interpolation approximate the radiative intensity field, the Piecewise Constant Angular scheme discretize the solid angle space, the Galerkin or Least squares weighted residual method discretize the spatial domain, the NEM for the radiative transfer equation is established. The numerical characteristics of the NEM are studied. The numerical test results show that, compared with Galerkin NEM, the Least squares NEM shows better numerical stability. To eliminate the "Ray effects" induced by the uneven heat load on the boundary, the separate calculation theory was adopted, in which the radiative intensities was divided into two parts, namely, the wall-emitting intensities and the medium-emitting intensities.The NEM investigation for the pure radiative heat transfer in the two-dimensional complex geometries with distinct refractive index is conducted. It is found that, due to the distinctive refractive index, the incident radiation on the interface is discontinuous. The NEM discretization scheme for the the nonlinear heat transfer boundary conditions is established. The combined radiative and conductive heat transfer in the two-dimensional participant media with complex geometries is studied. It is found that, the differences between the results by diffusely semitransparent boundary and opaque boundary are significant. With the semitransparent boundary surface, due to the transmission of the envirionment radiation, the temperature peak or valley appears near the boundary. The NEM is further extended to solve the three-dimensional radiative heat transfer problems. It is show that the NEM can be applied to solve the three-dimensional radiative transfer with complex geometries.The NEM appoarch for the transient radiative transfer in inhomogerous participant media with the short-pulsed irradiation is established. The diffuse intensities relations on the Fresnel interface are given and the NEM numerical model for the collimated intensities is developed. The numerical solution with high efficienty and precision for the transient radiative transfer in multi-layer media with Fresnel surface is realized. Based on this, transient radiative transfer problems in one-dimensional two-layer media is examined. It is found that, due to the interface reflection effects on the collimated lights, the step increase happens periodically in the reflectance signals. The research on the transient radiative transfer in two-dimensional uniform refractive index media with collimated and diffuse short-pulsed irradiation is conducted. The transient radiative transfer in gradient refractive index media with diffuse energy pulse irradiation is investigated. It is found that, effects of the monotone property of the gradient index on the time-resolved signals are significant.The NEM is extended to solve the steady vector radiative transfer problem in a multi-dimensional inhomogerous media. The problems in uniform media with different scattering type are solved. The numerical efficience and stability is examined. It is found that the NEM can be successfully used for solve vector radiative transfer problems with different scattering conditions. The linearly interpolation scheme for the diffuse Stokes vector on the Fresnel surface is given, and the numerical solution for the collimated Stokes vector is developed. Based on the multi-layer model, by setting enough number of the layers to approach the gradient index media, the problems in a gradient index media are studied. It is found that, effects of the monotone property of the gradient index on the Stokes vector are significant. The NEM is then further extended to solve the two-dimensional polarized radiative transfer. The problems in a scattering medium which is equivalent to a suspension of latex spheres in water is studied.The NEM appoarch for the transient vector radiative transfer in inhomogeneous media with short-pulsed irradiation is established. To shown the efficient and accuate of the model, the problem in a Mie scattering media is solved, and the MCM results from the literature are presented for comparison. Based on this, this paper studies the transient polarized radiative transfer in a scattering media subjected to the irradiation of a square pulse. Rayleigh scattering, Mie scattering and aerosol scattering and atmosphere-ocean problems are solved. The transient characteristics the time-resolve signals and the polarization properties of the Stokes vector are analyzed. It is found that, the distinction of the time-resolved signals by different scattering types is significant. Afterwards, the two-dimensional problems are investigated. The time-resolved signals and the polarized radiative flux on the boundaries are presented and discussed in detail.