An asymptotic preserving scheme for hydrodynamics radiative transfer models

In this paper, we present a numerical scheme for a hydrodynamics radiative transfer model consisting of two steps: the first one is based on a relaxation method and the second one on the well balanced scheme. The derivation of the scheme relies on the resolution of a stationary Riemann problem with source terms. The obtained scheme preserves the limited flux property and it is compatible with the diffusive regime of hydrodynamics radiative transfer models. These properties are illustrated by numerical tests, one of them involves a radiative transfer model coupled with an equation for the temperature of the material.     

TheF N method for radiative transfer problems without azimuthal symmetry

The formalism required to solve by theF _N method radiative transfer problems lacking azimuthal symmetry is developed, and numerical results are given.

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Zusammenfassung Es wird der Formalismus entwickelt der zur Lösung von Strahlungsproblemen mit derF _N -Methode benötigt wird, falls keine azimutale Symmetrie vorliegt. Numerische Ergebnisse werden gegeben.

     

On the differential approximation in radiative transfer

Zusammenfassung Die Anwendbarkeit des Differentialnäherungswertes bei der Berechnung der Wärmeübertragung durch Strahlung wird für verschiedene geometrische Konfigurationen geprüft. Es wird gezeigt, dass mit Ausnahme der eindimensionalen flachen Schicht der Differentialnäherungswert nur beschränkt verwendbar ist.

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This work was sponsored by the US Air Force, Office of Aerospace Research Aerospace Research Laboratories, under Contract AF 33(615)-3104. The author is indebted to Prof.L. S. Wang for several stimulating discussions.     

Weakly nonlinear interaction of two waves in radiative gasdynamics

The interaction of two weakly nonlinear waves in radiative gasdynamics is investigated following the perturbation analysis developed by He and Moodie. Explicit solutions are given and the two waves interactions are graphically shown.     

Meshless method for solving multidimensional radiative transfer in graded index medium

A diffuse approximation meshless (DAM) method is presented to solve the radiative transfer equation (RTE) in a graded index medium. The meshless method can solve the equation directly without using an upwind scheme. Absorbing, emitting and scattering media with different kinds of graded indices in 1D and 2D geometries are tested. Prediction results obtained by the proposed method are compared with different references in order to illustrate the performance of this solution method.     

On eigenvalue calculations for radiative transfer models that include polarization effects

Several representations of the dispersion matrix (z) basic to analytical solutions for a theory of radiative transfer that includes the effects of polarization are reported, and a method for computing the zeros of det (z) is discussed. Numerical results are given for several specific models.

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Zusammenfassung Verschiedene Darstellungen der Dispersionsmatrix (z), welche grundlegende Bedeutung für die analytischen Lösungen der Theorie der Strahlungsübertragung mit Polarisation hat, werden angegeben. Eine Methode zur Berechnung der Nullstellen von det (z) wird diskutiert. Es werden numerische Ergebnisse für verschiedene Modelle angegeben.

     

Adaptive computation for boundary control of radiative heat transfer in glass

This paper is concerned with an optimal boundary control of the cooling down process of glass, an important step in glass manufacturing. Since the computation of the complete radiative heat transfer equations is too complex for optimization purposes, we use simplified approximations of spherical harmonics including a practically relevant frequency bands model. The optimal control problem is considered as a constrained optimization problem. A first-order optimality system is derived and decoupled with the help of a gradient method based on the solution to the adjoint equations. The arising partial differential–algebraic equations of mixed parabolic–elliptic type are numerically solved by a self-adaptive method of lines approach of Rothe type. Adaptive finite elements in space and one-step methods of Rosenbrock-type with variable step sizes in time are applied. We present numerical results for a two-dimensional glass cooling problem.     

Existence and bounds for the half-moment entropy approximation to radiative transfer

We establish existence, uniqueness and a priori bounds for the half-moment entropy approximation to radiative heat transfer. The bounds are physically reasonable and underline the approximation properties of the system. We show numerical results to illustrate the bounds.     

Functional optimization technique for numerical solution of the radiative transfer equation

A numerical method for solving the time-independent radiative transfer problem in a flat layer with given properties and temperature distribution is proposed. This method avoids the numerical diffusion; rather, it is based on a gradient procedure for the functional minimization of the residual of the radiative transfer integral equation. Means for suppressing computational instabilities are proposed that reduce requirements for the approximation of the operators in the optimization problem but do not change the problem objective functional.     

The propagation of electromagnetic waves in parabolic wave guides

Résumé Dans cet exposé, l'auteur examine les propriétés de canaux qui propagent les ondes électromagnétiques. Les parois de ces canaux sont faites d'une paire de paraboles orthogonales. L'auteur donne des expressions obtenues pour les fréquences critiques dans le cas de canaux parfaitement conducteurs, ainsi que des formules nouvelles par lesquelles on peut évaluer les constantes d'atténuation dans le cas de canaux imparfaitement conducturs.     

Some classes of electromagnetic waves that admit parabolic helices

We describe classes of electromagnetic waves that admit the subgroups of the Poincaré group such that the subgroups contain parabolic helices. Representatives of some classes are constructed. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 79–92, 2006.     

Positively homogeneous functions in atmospheric radiative transfer theory

Positively homogeneous functions are applied to describe absorption and scattering processes within the framework of atmospheric radiative transfer theory. Solid angle integrations are understood as surface integrations over arbitrary solid angle surfaces which are defined beyond the common picture of atmospheric radiative transfer.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.     

The cauchy problem for the radiative transfer equation with generalized conjugation conditions

The initial boundary problem for the nonstationary radiative transfer equation in a nonhomogeneous plane layer with generalized conjugation conditions on the material interface is studied. A generalized Monte Carlo algorithm is proposed for solving the problem, and numerical experiments are discussed.     

Asymptotic-preserving &; well-balanced schemes for radiative transfer and the Rosseland approximation

Summary. We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow the Well-Balanced approachs canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type tO(x²) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.Mathematics Subject Classification (1991): 82C70, 65M06, 35B25Work partially supported by EEC network #HPRN-CT-2002-00282.Revised version received July 21, 2003