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COMPUTATIONAL EFFICIENCY OF THE FINITE ELEMENT METHOD BASED ON THE SECOND-ORDER RADIATIVE TRANSFER EQUATION

DOI: 10.1615/ICHMT.2010.RAD-6.380
10 pages

Junming Zhao
School of Energy Science and Engineering, Harbin Institute of Technology 92 West Dazhi Street, Harbin, 150001, People's Republic of China

Jianyu Tan
Harbin Institute of Technology at Weihai, Harbin Institute of Technology, 2 West Wenhua Road, Weihai 264209, P.R. China

Linhua Liu
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China; School of Energy and Power Engineering, Shandong University, Qingdao 266237, China

Resumo

The second-order radiative transfer equation (SORTE) [Numerical Heat Transfer B, Vol. 51, pp. 391-409, 2007] is in a form like diffusion equation, hence no additional artificial diffusion or upwinding treatment is needed in the numerical discretization for stabilization. The computational efficiency of the finite element method based on SORTE is investigated by comparison with that of the finite element methods based on original first order radiative transfer equation (FORTE). The FORTE based finite element methods considered are the finite element method with Galerkin approach (Galerkin-FORTE) and the finite element method with least-square approach (LS-FORTE). By comparison, the accuracy of the finite element method based on the SORTE is generally better than those based on the FORTE under the same discretization scheme, spatial grid and angular grid. The finite element method based on the SORTE shows the best computational efficiency among the three finite element methods, i.e., to obtain the same target accuracy, the least computational time is required.

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