Multi-scale Analysis for Rosseland Equation with Small Periodic Oscillating Coefficients

TL;DR

This paper develops a multi-scale analysis framework for Rosseland equations with small periodic oscillating coefficients, establishing well-posedness, algorithms, and asymptotic expansions for heat transfer modeling in optically thick media.

Contribution

It provides the first comprehensive theoretical and computational analysis of Rosseland equations with small periodic coefficients, including well-posedness, algorithms, and asymptotic expansions.

Findings

Proved global well-posedness of Rosseland-type equations.

Presented convergent algorithms for solving these equations.

Derived and analyzed second-order two-scale asymptotic expansions.

Abstract

Rosseland equation is one of the most popular models of the conduction-radiation coupled heat transfer in the thermal protection system. The well-posedness, the corresponding mathematical theory and the Multi-scale analysis method for the Rosseland-type equations with small periodic oscillating coefficients are concerned, which provides a theoretical basis for the Multi-scale computation of the conduction-radiation coupled heat transfer in an optically thick medium with a small periodic structure. The global well-posedness of the Rosseland-type (parabolic) equations is given in the first part. The corresponding solving algorithms and their convergence analysis are presented in the second part. In the third part we study the well-posedness and the second-order two-scale asymptotic expansion of the Rosseland-type (elliptic) equations with small periodic oscillating coefficients. The convergence analysis of the second-order two-scale asymptotic expansion is studied in the last part.