New rotated iterative algorithms for the solution of a coupled system of elliptic equations

Abstract

Iterative method based on the rotated finite difference approximations has been shown to be much faster than the method based on the standard five-point formula in solving elliptic p.d.e.'s, which is due to the former's overall lower computational complexity [1]. In this paper, iterative methods derived on the rotated formulae for solving a coupled system of elliptic p.d.e.'s are described. The time-independent case is treated, in particular the steady-state Navier-Stokes equations. Both point and group iterative schemes will be discussed. Numerical results obtained reveal that the iterative method based on the group scheme converge more rapidly than the pointwise scheme which were in agreement with their computational complexity analysis.

Keywords:

• Navier-Stokes equations
• explicit decoupled group (EDG) method
• rotated finite difference
• point iterative scheme
• group iterative scheme

C.R. Categories:

• G.1.8