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Technical Briefs

The Efficient Iterative Solution of the P1 Equation

[+] Author and Article Information
P. Hassanzadeh

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

G. D. Raithby1

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadagraith@mecheng1.uwaterloo.ca

1

Corresponding author.

J. Heat Transfer 131(1), 014504 (Oct 22, 2008) (3 pages) doi:10.1115/1.2993546 History: Received December 03, 2007; Revised July 11, 2008; Published October 22, 2008

The P1 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 P1 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 P1 equation.

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Grahic Jump Location
Figure 1

Maximum scaled residuals versus iterations for (a) τ=0.01 and (b) τ=10

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