An under‐relaxation factor control method for accelerating the iteration convergence of flow field simulation

Abstract

Purpose

This paper aims to accelerate the iteration convergence for elliptic fluid flow problems, so that an under‐relaxation factor control method is developed.

Design/methodology/approach

There should be an optimal under‐relaxation factor that can result in the equivalence of the global residual norms of momentum equation u and momentum equation v. The two residual norms of the momentum equations will be equivalent through controlling the velocity under‐relaxation factors, and then the iteration convergence can be accelerated. Two expressions (α=(α⁰)^βγ and α=(α⁰)^(1/β)γ) are proposed to adjust the values of under‐relaxation factors for every n iterations.

Findings

From the five preliminary computations it is found that the value of γ can be larger than 1 and of n can be less than 5 for an open system, and the value of γ should be less than 1 and that of n should be larger than 10 for a closed system. These two pairs of parameters are then used in another five examples. It is found that the saving in CPU times is at least 43.9 percent for the closed system and 67.5 percent for the open system.

Research limitations/implications

When the Re or Ra of the two‐dimensional problems are low, this control method is feasible. More research work is needed in order to apply it in three‐dimensional or high Re or Ra problems.

Originality/value

This method is helpful for the acceleration of iteration convergence in simple problems, and is a preparation for the advanced research in complicated problems.

Citation

Min, C.H. and Tao, W.Q. (2007), "An under‐relaxation factor control method for accelerating the iteration convergence of flow field simulation", Engineering Computations, Vol. 24 No. 8, pp. 793-813. https://doi.org/10.1108/02644400710833314