An Investigation of 2D/1D Approximations to the 3D Boltzmann Transport Equation.

2D/1D;transport;diffusion;Fourier analysis;Nuclear Engineering and Radiological Sciences;Engineering;Nuclear Engineering & Radiological Sciences and Scientific Computing

Kelley, Blake W.Martin, William R. ;

University of Michigan

关键词: 2D/1D;    transport;    diffusion;    Fourier analysis;    Nuclear Engineering and Radiological Sciences;    Engineering;    Nuclear Engineering & Radiological Sciences and Scientific Computing;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/113576/kelleybl_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

A new class of ;;2D/1D;;approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and employ approximate diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions are more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this work, we (i) introduce several new ;;2D/1D equations;; as accurate approximations to the 3D Boltzmann transport equation, (ii) show that the 2D/1D equations have certain desirable properties, (iii) systematically discretize the equations, and (iv) derive a stable iteration scheme for solving the discrete system of equations. Additionally, we give numerical results that confirm the theoretical predictions of accuracy and iterative stability.