Finite element approximations for the radiative transfer equation

2006 ◽  
Author(s):  
Marko Vauhkonen ◽  
Tanja Tarvainen ◽  
Ville Kolehmainen ◽  
Jari P. Kaipio
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Finite Element Approximations

A New Stabilized Finite Element Formulation for Solving Radiative Transfer Equation

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
L. Zhang ◽  
J. M. Zhao ◽  
L. H. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Second Order ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Stabilized Finite Element ◽  
Element Method

A new stabilized finite element formulation for solving radiative transfer equation is presented. It owns the salient feature of least-squares finite element method (LSFEM), i.e., free of the tuning parameter that appears in the streamline upwind/Petrov–Galerkin (SUPG) finite element method. The new finite element formulation is based on a second-order form of the radiative transfer equation. The second-order term will provide essential diffusion as the artificial diffusion introduced in traditional stabilized schemes to ensure stability. The performance of the new method was evaluated using challenging test cases featuring strong medium inhomogeneity and large gradient of radiative intensity field. It is demonstrated to be computationally efficient and capable of solving radiative heat transfer in strongly inhomogeneous media with even better accuracy than the LSFEM, and hence a promising alternative finite element formulation for solving complex radiative transfer problems.

A MIXED VARIATIONAL FRAMEWORK FOR THE RADIATIVE TRANSFER EQUATION

2012 ◽  
Vol 22 (03) ◽  
pp. 1150014 ◽  
Author(s):  
HERBERT EGGER ◽  
MATTHIAS SCHLOTTBOM
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Variational Method ◽  
Weak Solutions ◽  
Transfer Equation ◽  
Existence And Uniqueness ◽  
Radiative Transfer Equation ◽  
Strong Solutions ◽  
Galerkin Methods ◽  
Variational Framework

We present a rigorous variational framework for the analysis and discretization of the radiative transfer equation. Existence and uniqueness of weak solutions are established under rather general assumptions on the coefficients. Moreover, weak solutions are shown to be regular and hence also strong solutions of the radiative transfer equation. The relation of the proposed variational method to other approaches, including least-squares and even-parity formulations, is discussed. Moreover, the approximation by Galerkin methods is investigated, and simple conditions are given, under which stable quasi-optimal discretizations can be obtained. For illustration, the approximation by a finite element PN approximation is discussed in some detail.

Sign in / Sign up

Export Citation Format

Share Document