1990 Volume 32 Issue 10 Pages 999-1008
Since numerical stability and accuracy of solutions are much affected by difference methods for convection terms of transport equations, many methods have been proposed to solve fluid flows efficiently. In recent years, higher-order upstream difference methods have been recognized as accurate methods for solving high Reynolds number flows. There is however little information on the conditions for the occurrence of numerical instability or numerical oscillation when the higher-order difference methods are adopted. In the present study, spectral radii and spectral norms of difference operators were examined analytically or numerically·to make the stability conditions of four higher-order difference methods clear. For the one-dimentional linear transport equation under various boundary conditions, the necessary and sufficient conditions of the stability defined by Lax & Richtmyer were derived using the spectral norms, and those of the stability defined by the boundedness of the solution as time nears infinity were obtained using the spectral radii. It was also shown by examination of eigenvalues of the spatial difference operators that the higher-order difference methods are subject to numerical oscillation when the cell Reynolds number exceeds a value of about two.
