Application of high‐order spatial resolution schemes to the hybrid finite volume/finite element method for radiative transfer in participating media

2008 ◽  
Vol 18 (2) ◽  
pp. 173-184 ◽  
Author(s):  
P.J. Coelho ◽  
D. Aelenei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Finite Volume ◽  
Spatial Resolution ◽  
High Order ◽  
Participating Media ◽  
Element Method

Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method

2013 ◽  
Vol 392 ◽  
pp. 100-104 ◽  
Author(s):  
Fareed Ahmed ◽  
Faheem Ahmed ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Discontinuous Galerkin ◽  
Finite Volume ◽  
High Order ◽  
Numerical Predictions ◽  
Volume Method ◽  
Element Method

In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.

Accelerate Iteration of Least-Squares Finite Element Method for Radiative Heat Transfer in Participating Media With Diffusely Reflecting Walls

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Wei An ◽  
Tong Zhu ◽  
NaiPing Gao
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Radiative Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Present Model ◽  
Participating Media ◽  
Element Method

A high reflectivity of walls often leads to prohibitive computation time in the numerical simulation of radiative heat transfer. Such problem becomes very serious in many practical applications, for example, metal processing in high-temperature environment. The present work proposes a modified diffusion synthetic acceleration model to improve the convergence of radiative transfer calculation in participating media with diffusely reflecting boundary. This model adopts the P1 diffusion approximation to rectify the scattering source term of radiative transfer equation and the reflection term of the boundary condition. The corrected formulation for boundary condition is deduced and the algorithm is realized by finite element method. The accuracy of present model is verified by comparing the results with those of Monte Carlo method and finite element method without any accelerative technique. The effects of emissivity of walls and optical thickness on the convergence are investigated. The results indicate that the accuracy of present model is reliable and its accelerative effect is more obvious for the optically thick and scattering dominated media with intensive diffusely reflecting walls.

Discontinuous Finite Element Approach for Transient Radiative Transfer Equation

2007 ◽  
Vol 129 (8) ◽  
pp. 1069-1074 ◽  
Author(s):  
L. H. Liu ◽  
L. J. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Scattering Media ◽  
Participating Media ◽  
Element Discretization ◽  
Discontinuous Finite Element ◽  
Transfer Problems ◽  
Discontinuous Finite Element Method ◽  
Element Method

A discontinuous finite element method based on the discrete ordinates equation is extended to solve transient radiative transfer problems in absorbing, emitting, and scattering media. The fully implicit scheme is used to discretize the transient term. Three numerical examples are studied to illustrate the performance of this discontinuous finite element method. The numerical results are compared to the other benchmark approximate solutions. By comparison, the results show that the discontinuous finite element method is efficient, accurate, and stable, and can be used for solving transient radiative transfer problems in participating media. Because the continuity at interelement boundaries is relaxed in discontinuous finite element discretization so that field variable is considered discontinuous across the element boundaries. This feature makes the discontinuous finite element method able to predict the correct propagation speed within medium and accurately capture the sharp drop in the incident radiation and the radiative heat flux at the penetration front.

A Mixed-Mesh and New Angular Space Discretization Scheme of Discontinuous Finite Element Method for Three-Dimensional Radiative Transfer in Participating Media

2005 ◽  
Vol 127 (11) ◽  
pp. 1236-1244 ◽  
Author(s):  
X. Cui ◽  
B. Q. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Three Dimensional ◽  
Scattering Media ◽  
Participating Media ◽  
Discontinuous Finite Element ◽  
Space Discretization ◽  
Discontinuous Finite Element Method ◽  
Element Method

This paper presents a discontinuous finite element method for the numerical solution of internal thermal radiation problems in three-dimensional (3D) geometries using an unstructured mesh of mixed elements. Mathematical formulation, numerical implementation, and computational details are given. The different domain discretization methods are presented, and a new angular space discretization is also given. Numerical examples are presented for 3D radiative transfer in emitting, absorbing, and scattering media. Computed results compare well with analytical solutions whenever available. The localized formulation intrinsic in discontinuous finite elements is considered particularly useful for computational radiation heat transfer in participating media.

Sign in / Sign up

Export Citation Format

Share Document