圧力のポアソン方程式におけるSOR法の最適加速係数

概要

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Computational time for numerical simulation of transient incompressible viscous flow is governed by numerical methods to solve the Poisson equation of the pressure. In order to improve the computational efficiency of the SOR method, a mathematical analysis was conducted in the present study to derive the spectral radius, i. e., the maximum modulus of the eigenvalues of the iteration matrix for a discrete Poisson equation in staggered mesh system. The derived spectral radii for the point, line and area Jacobi iteration matrices are applicable to the Dirichlet, the mixed boundaryvalue and the Neumann problems in an n-dimensional rectangular region. The validity of the optimum relaxation parameter of the SOR method, which was calculated by the derived spectral radii, was confirmed by numerical experiments. Furthermore, a simple estimation method of the optimum relaxation parameter for the non-rectangular region was presented for transient flow analyses.
1992-07-25