An Energy Stable SPH Method for Incompressible Fluid Flow

作     者：Xingyu Zhu Shuyu Sun Jisheng Kou 

作者机构：Computational Transport Phenomena LaboratoryDivision of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwal 23955-6900Saudi Arabia School of Civil EngineeringShaoxing UniversityShaoxing 312000ZhejiangChina School of Mathematics and StatisticsHubei Engineering UniversityXiaogan 432000HubeiChina 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2022年第14卷第5期

页      面：1201-1224页

核心收录：

学科分类：083002[工学-环境工程] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 08[工学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：This work is partially supported by King Abdullah University of Science and Technology(KAUST)through the grants BAS/1/1351-01 URF/1/4074-01 and URF/1/3769-01. 

主　　题：Particle method Smoothed Particle Hydrodynamics(SPH)method incompressible fluid flow energy stability numerical stability 

摘      要：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.