Acceleration of Unsteady Incompressible Flow Calculation Using Extrapolation Methods

Abstract

Extrapolation methods constitute a class of acceleration techniques in which the converged solution is predicted from a series of intermediate solutions generated by the iterative method. Advantages of the extrapolation methods are simplicity and ease of the implementation in existing CFD codes. In this study, the authors apply Minimal Polynomial Extrapolation (MPE) to 2-D laminar and 3-D turbulent problems to examine the performance of MPE in unsteady flow calculation. Also Initial Extrapolation (IE), which provides a good initial guess at the start of each timestep, is tested alongside MPE. Although only six intermediate solutions are used in MPE, it realizes reasonable speed-ups : 2.88 in the 2-D calculation and 1.89 in the 3-D LES. This computational cost is far lower than that in steady calculation reported in a literature. Furthermore, the combination of IE and MPE shows larger acceleration effects than in the case of single application of MPE because the speed-ups by the joint application of the two extrapolation methods reach 4.41 in the 2-D and 2.33 in the 3-D.