The Research On Diffusion Approximation Method For Solving The Radiative Transfer Equation

Radiation,as a way of transmitting energy and information,has been widely applied in many high-tech fields,such as military and civilian.It has been applied to electromagnetics,atmospheric science,combustion,oceanography and Aeronautics and Astronautics in addition to the most widely used thermo and optics.With the rapid development of laser pulse technology,the time of laser pulse has reached the level of femtosecond.For the incident of ultrashort laser,the change of radiation intensity within the medium can not be ignored,which makes this kind of problem more complex than the traditional steady state radiation transmission.Because of the complexity of transient radiation transmission,theoretical analysis is limited to a few simple problems,most of which are studied by experiment and numerical simulation,and experimental research needs a variety of physical parameters and a large number of data.Therefore,numerical methods are used to solve and analyze the transient radiation process as an important means of research by scholars in various countries.Accurate and efficient algorithm for solving radiative transfer problem in participatory media has become an important research content.Based on the radiative transfer equation solved by the diffusion approximation method,the problems of steady state radiation transfer,transient time domain,transient frequency domain optical signal simulation,and the inversion of the internal parameters of the medium are systematically studied.The main work is summed up in the following four aspects:1.To solve the steady-state diffusion equation based on a two-dimensional physical model,considering the influence of refractive index,optical thickness,wall emissivity,albedo scattering coefficient of diffusion approximation accuracy.The Fortran program is used to calculate the non dimensional radiation heat flow distribution at the bottom of the medium,and the results are compared with the results of the Monte Carlo algorithm.On this basis,the influence scope of each optical parameter on the approximate accuracy of diffusion is analyzed,and the influence degree of the optical parameter is further explored.It provides data reference for improving the approximate accuracy of diffusion effectively.2.Participate in the establishment of one-dimensional transient medium radiation transfer model,by comparing with the discontinuous finite element method,and verify the accuracy of the diffusion approximation method is discussed,analyzed the gradient refractive index change of transmittance and reflectance effect on time domain,and the gradient index medium based research in medium optical thickness,scattering albedo effect the rate of the wall surface,the emission rate and the pulse width of the time-domain transmittance and reflectance,provide a reference for the study of diffusion approximation method in transient radiation.3.The frequency domain diffusion approximation method is developed.First,based on the homogeneous refractive index medium,the frequency domain diffusion approximate coupling equations are solved,and the frequency domain penetration and the frequency domain reflectivity are calculated.The optical thickness,scattering albedo,change value and pulse width as the change in value,study the diffusion effect the accuracy of the approximation of the frequency domain;secondly in inhomogeneous media as the research content,the refractive index changes as the value analysis of diffusion approximation method in the applicable conditions of gradient index medium.4.Based on the transient time domain diffusion approximation simulation,the conjugate gradient method is applied to calculate the refractive index distribution of the medium,and the influence of the refractive index of the medium on the accuracy of the inversion is analyzed.