Year: 2022
Author: Xingyu Zhu, Shuyu Sun, Jisheng Kou
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1201–1224
Abstract
In this paper, a novel unconditionally energy stable Smoothed Particle Hydrodynamics (SPH) method is proposed and implemented for incompressible fluid flows. In this method, we apply operator splitting to break the momentum equation into equations involving the non-pressure term and pressure term separately. The idea behind the splitting is to simplify the calculation while still maintaining energy stability, and the resulted algorithm, a type of improved pressure correction scheme, is both efficient and energy stable. We show in detail that energy stability is preserved at each full-time step, ensuring unconditionally numerical stability. Numerical examples are presented and compared to the analytical solutions, suggesting that the proposed method has better accuracy and stability. Moreover, we observe that if we are interested in steady-state solutions only, our method has good performance as it can achieve the steady-state solutions rapidly and accurately.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0231
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1201–1224
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Particle method Smoothed Particle Hydrodynamics (SPH) method incompressible fluid flow energy stability numerical stability.
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