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Transport Phenomena in Thermal Engineering. Volume 2

ISBN:
1-56700-015-0 (Print)

A PRACTICAL APPLICATION OF THE INCOMPLETE CHOLESKEY-DECOMPOSITION CONJUGATE GRADIENT METHOD TO LARGE EDDY SIMULATION INNER-BOUNDARY PROBLEMS

Sae Yul Lee
Nuclear Engineering Department, Texas A&M University, College Station, TX 77843, USA

Yassin A. Hassan
Department of Nuclear Engineering, Texas A&M University, College Station, TX 77843, USA

Abstract

The objective of this study is to investigate a time and memory saving solution algorithm for inner boundary fluid flow problems, such as flow within the steam generator tube bundle region. In most algorithms for the numerical solution of the Navier-Stokes equations, a pressure correction equation (a Poisson equation) must be solved to ensure mass conservation. The pressure correction coefficient matrix is sparse and usually quite large; most of calculational effort is spent solving the matrix equations. The Choleskey decomposition method, which is one of the most effective direct solvers, showed difficulties in computational time and storage for the calculation of practical bundle problems. To avoid the problems inherent in direct solvers, the Incomplete Choleskey-decomposition Conjugate Gradient (ICCG) method was adopted as the Poisson equation solver. There are several efficient techniques for solving large sparse matrices, but the advantages of these techniques disappear when applied to inner boundary problems. The pressure coefficient matrix of inner boundary problems has an irregular pattern of non-zero elements. A preconditioning technique must be developed in order to apply the ICCG method to flow problems with varied boundary conditions. In this study, the coefficient matrix is scanned column-wise.
Non-zero elements and their positions are stored in band arrays regardless of their relative position in the original matrix. This scanning generates new band arrays which can be applied to any kind of boundary problem. The ICCG method with the above preconditioning showed significant memory savings, while calculational time and accuracy are comparable with the direct solver. It was also found that memory savings increases as the problem size increases.