The model is often used to obtain approximate solutions of the radiative transfer equation for heat transfer in a participating medium. For large problems, the algebraic equations used to obtain the solution are solved by iteration, and the convergence rate can be very slow. This paper compares the performance of the corrective acceleration scheme of and Li and Modest (2002, “A Method to Accelerate Convergence and to Preserve Radiative Energy Balance in Solving the P1 Equation by Iterative Methods,” ASME J. Heat Transfer, 124, pp. 580–582), and the additive correction multigrid method, to that of the Gauss–Seidel solver alone. Additive correction multigrid is found to outperform the other solvers. Hence, multigrid is a superior solver for the equation.
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The Efficient Iterative Solution of the Equation
P. Hassanzadeh,
P. Hassanzadeh
Department of Mechanical and Mechatronics Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
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G. D. Raithby
G. D. Raithby
Department of Mechanical and Mechatronics Engineering,
e-mail: graith@mecheng1.uwaterloo.ca
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
Search for other works by this author on:
P. Hassanzadeh
Department of Mechanical and Mechatronics Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
G. D. Raithby
Department of Mechanical and Mechatronics Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canadae-mail: graith@mecheng1.uwaterloo.ca
J. Heat Transfer. Jan 2009, 131(1): 014504 (3 pages)
Published Online: October 22, 2008
Article history
Received:
December 3, 2007
Revised:
July 11, 2008
Published:
October 22, 2008
Citation
Hassanzadeh, P., and Raithby, G. D. (October 22, 2008). "The Efficient Iterative Solution of the Equation." ASME. J. Heat Transfer. January 2009; 131(1): 014504. https://doi.org/10.1115/1.2993546
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