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An Energy Stable SPH Method for incompressible fluid flow

Advances in Applied Mathematics and Mechanics 2022年第5期14卷 1201-1224页

作者： Xingyu Zhu Shuyu Sun Jisheng Kou Computational Transport Phenomena Laboratory Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwal 23955-6900Saudi Arabia School of Civil Engineering Shaoxing UniversityShaoxing 312000ZhejiangChina School of Mathematics and Statistics Hubei Engineering UniversityXiaogan 432000HubeiChina

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.

关键词： Particle method Smoothed Particle Hydrodynamics(SPH)method incompressible fluid flow energy stability numerical stability

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ERROR ESTIMATION OF PREDICTION-CORRECTION LEGENDRE SPECTRAL APPROXIMATION TO incompressible fluid flow

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Acta Mathematicae Applicatae Sinica 2000年第3期16卷 245-257页

作者：贺力平郭本瑜茅德康 Department of Applied Mathematics Shanghai Jiao Tong University Shanghai China Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Shanghai University Shanghai China

The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It is strictly proved that the numerical solution possesses the accuracy of second-order in time and higher order in space.

关键词： incompressible fluid flow stream function form high accuracy convergence prediction-correction Legendre spectral approximation

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