Nonlinear Radiative Transfer Research Articles

On coupled conductive-radiative heat-transfer problems in a sphere

A sphere-to-plane transformation technique and the spherical harmonics method are used, along with Hermite cubic splines, to define an iterative technique for solving a class of nonlinear radiative transfer problems in a sphere. Computational aspects of the technique are discussed, and the method is used to establish numerical results for several test problems.

Solution of the Nonlinear Radiative Transfer Equations by a Fully Implicit Matrix Monte Carlo Method Coupled with the Rosseland Diffusion Equation via Domain Decomposition

In this article, a new fully implicit Monte Carlo method for solving the nonlinear radiative transfer equations is presented. This scheme is both temperature and frequency implicit, and the particle tracking is much faster than in the standard Fleck method. This tracking is used to build an energy balance matrix. This leads to an original matrix formulation of the energy balance equation, where the entries of the matrix are computed by a Monte Carlo method. This matrix formulation of the energy balance equation allows this method to be easily coupled with the Rosseland diffusion equation, which is generally needed in optically thick media, via domain decomposition. This coupling scheme between the two methods is also fully implicit. Numerical tests are shown to prove the efficiency of the matrix Monte Carlo method; the results are better than those obtained by Fleck’s method in that there are smaller computation times and there is a better robustness of the time discretization.

View-factor method for solving time-dependent radiation transport problems involving fixed surfaces with intervening, participating media

A description is given of a view factor technique for solving time-dependent, non-linear radiative transfer problems. It is believed unique among view factor methods in having the ability to solve problems involving gases or plasmas with emissive and absorptive characteristics which vary in space and time. The radiative characteristics of the enclosing surfaces can also have an arbitrary space and time dependence, and these characteristics can be updated based on an appropriate physical model of the interaction of the background radiation field with the medium. Various sample problems are solved, including a time-dependent solution for concentric spheres filled with a participating medium of arbitrary opacity for a step function source.

Analysis of a Monte Carlo method for nonlinear radiative transfer

It has recently been proved that solutions of nonlinear radiative transfer problems satisfy a maximum principle (Andreev, Kozmanov, and Rachilov, U.S.S.R. Comput. Math. Math. Phys. 23, 104 (1983); Mercier, SIAM J. Math. Anal., in press). In this article it is shown that Monte Carlo solutions of such problems, obtained using the method of Fleck and Cummings ( J. Comput. Phys. 8, 313 (1971)), must satisfy this maximum principle for sufficiently small time-steps, but can violate it for sufficiently large time-steps. Analyses of the frequency-dependent and grey cases are given, and a numerical solution violating the maximum principle is discussed.

Iterative algorithms for nonlinear problems in remote sensing

First a brief review of the Backus and Gilbert method for the linear problems is given. Then a comprehensive presentation of iterative algorithms for constructing approximate solutions of nonlinear problems from erroneous inadequate data is given. Proofs of convergence and error estimates of these iterative algorithms are obtained. It is found that locally the limit of the iterates does not satisfy the original nonlinear operator equation, but a somewhat different nonlinear equation which depends on the initial iterate. A nonlinear radiative transfer equation in remote sensing of the atmospheric temperature profiles is used as an example to demonstrate the applicability of the iterative algorithms. Finally, a discussion of the present status of research in this domain and some personal views on what should be the useful lines for future research is given.

Numerical solutions of a nonlinear radiative transfer equation with inadequate data

Iterative algorithms for solving numerically a nonlinear radiative transfer equation with inadequate data are presented and tested by numerical simulations. It is found that these iterative algorithms do give excellent results.

Two-dimensional radiative transfer by synthesis methods

The synthesis method is suggested for solving two-dimensional, time dependent, nonlinear radiative transfer problems. Synthesis is an attempt to reduce computer time requirements substantially for two-dimensional radiation transport by accurately constructing the two-dimensional problem from a small number of one-dimensional calculations. The method is explicitly developed for the nonequilibrium diffusion of radiation in cartesian coordinates, but is applicable to any description of radiative transfer in arbitrary geometry. Grey radiative transfer is assumed with no scattering although these assumptions are not essential to the method. Results indicate that synthesis is remarkably accurate; relatively few one-dimensional calculations are needed to represent the real two-dimensional problem.

On a problem in nonlinear radiative transfer

On a problem in nonlinear radiative transfer