TY - JOUR

T1 - Investigation of high speed calculation method of matrix equations disretized by finite volume method

AU - Matsushita, Yohsuke

AU - Sugawara, Kosei

AU - Miyauchi, Shinsuke

AU - Morozumi, Yoshio

AU - Aoki, Hideyuki

AU - Miura, Takatoshi

PY - 2005/5/1

Y1 - 2005/5/1

N2 - A fast and stable solution of matrix equations formed by a finite volume method as a discretization scheme was investigated in steady flow calculation, especially with non-computational cells and cyclic conditions often used in cylindrical coordinate systems. To simulate a computational domain having complex geometry, a method was developed to form a coefficient matrix discretized by a finite volume method. The matrix equations were iteratively solved by the Bi-Conjugate Gradient Stabilized method with polynomial preconditioning (Bi-CGSTAB), and the calculated results were compared with those given by the Tri-Diagonal Matrix Algorithm (TDMA). Convergence and stability of the iterative calculation and under-relaxation factors are also discussed. No differences between TDMA and Bi-CGSTAB for a solution of matrix equations were found in the calculated results. With a greater number of computational cells, faster convergence was obtained by Bi-CGSTAB than by TDMA. Furthermore, larger under-relaxation factors could be employed for the calculation of Bi-CGSTAB than that of TDMA. Bi-CGSTAB is superior to TDMA giving in fast and stable convergence as a solution of the matrix equations discretized by a finite volume method. Therefore, stable calculation and fast convergence can be obtained using the present method.

AB - A fast and stable solution of matrix equations formed by a finite volume method as a discretization scheme was investigated in steady flow calculation, especially with non-computational cells and cyclic conditions often used in cylindrical coordinate systems. To simulate a computational domain having complex geometry, a method was developed to form a coefficient matrix discretized by a finite volume method. The matrix equations were iteratively solved by the Bi-Conjugate Gradient Stabilized method with polynomial preconditioning (Bi-CGSTAB), and the calculated results were compared with those given by the Tri-Diagonal Matrix Algorithm (TDMA). Convergence and stability of the iterative calculation and under-relaxation factors are also discussed. No differences between TDMA and Bi-CGSTAB for a solution of matrix equations were found in the calculated results. With a greater number of computational cells, faster convergence was obtained by Bi-CGSTAB than by TDMA. Furthermore, larger under-relaxation factors could be employed for the calculation of Bi-CGSTAB than that of TDMA. Bi-CGSTAB is superior to TDMA giving in fast and stable convergence as a solution of the matrix equations discretized by a finite volume method. Therefore, stable calculation and fast convergence can be obtained using the present method.

KW - Bi-CGSTAB

KW - Finite Volume Method

KW - Matrix Solution

KW - Numerical Simulation

KW - TDMA

UR - http://www.scopus.com/inward/record.url?scp=22944432217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22944432217&partnerID=8YFLogxK

U2 - 10.1252/kakoronbunshu.31.177

DO - 10.1252/kakoronbunshu.31.177

M3 - Article

AN - SCOPUS:22944432217

VL - 31

SP - 177

EP - 184

JO - Kagaku Kogaku Ronbunshu

JF - Kagaku Kogaku Ronbunshu

SN - 0386-216X

IS - 3

ER -