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Open AccessArticle

Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow

by Shuai Ye 1,†, Yufei Lin 2,*, Liyang Xu 1 and Jiaming Wu 3
1
State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China
2
National Innovation Institute of Defense Technology, Beijing 100071, China
3
Advanced Institute of Engineering Science for Intelligent Manufacturing, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Current address: No.109 Deya Rd, Kaifu District, Changsha, Hunan, China.
Mathematics 2020, 8(1), 119; https://doi.org/10.3390/math8010119
Received: 2 December 2019 / Revised: 5 January 2020 / Accepted: 8 January 2020 / Published: 13 January 2020
The pressure equation, generated while solving the incompressible Navier–Stokes equations with the segregated iterative algorithm such as PISO, produces a series of linear equation systems as the time step advances. In this paper, we target at accelerating the iterative solution of these linear systems by improving their initial guesses. We propose a weighted group extrapolation method to obtain a superior initial guess instead of a general one, the solution of the previous linear equation system. In this method, the previous solutions that are used to extrapolate the predicted solutions are carefully organized to address the oscillatory solution on each grid. The proposed method uses a weighted average of the predicted solutions as the new initial guess to avoid over extrapolating. Three numerical test results show that the proposed method can accelerate the iterative solution of most linear equation systems and reduce the simulation time up to 61.3%. View Full-Text
Keywords: incompressible Navier–Stokes equations; segregated iterative algorithm; linear equation system; initial guess; iterative method incompressible Navier–Stokes equations; segregated iterative algorithm; linear equation system; initial guess; iterative method
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Ye, S.; Lin, Y.; Xu, L.; Wu, J. Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow. Mathematics 2020, 8, 119.

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