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

Yohsuke Matsushita, Kosei Sugawara, Shinsuke Miyauchi, Yoshio Morozumi, Hideyuki Aoki, Takatoshi Miura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)177-184
Number of pages8
Journalkagaku kogaku ronbunshu
Issue number3
Publication statusPublished - 2005 May 1


  • Finite Volume Method
  • Matrix Solution
  • Numerical Simulation
  • TDMA

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)


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