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      |本期目錄/Table of Contents|

       ZHANG Kai,SUN Zhongguo,XI Guang.Influence of the Kernel Function Characteristics on the Stability of Pressure Solution of Moving Particle Semi-Implicit Method[J].Journal of Xi'an Jiaotong University,2019,53(09):1-6+25.[doi:10.7652/xjtuxb201909001]





      Influence of the Kernel Function Characteristics on the Stability of Pressure Solution of Moving Particle Semi-Implicit Method
      張凱 孫中國 席光
      西安交通大學能源與動力工程學院, 710049, 西安
      ZHANG Kai SUN Zhongguo XI Guang
      School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
      移動粒子半隱式法 核函數 壓力振蕩 靜水壓力 液體晃動
      moving particle semi-implicit method kernel function pressure oscillation hydrostatic pressure liquid sloshing
      O241; O354.5
      針對移動粒子半隱式法在求解特定問題時,壓力求解可能會出現一定程度的波動,分析了移動粒子半隱式法中核函數曲線形狀特征對壓力求解穩定性的影響,構造了一種指數多項式型核函數。模擬了典型靜壓(靜水壓力問題)和動壓(液體晃動問題)算例,并將模擬結果與理論解或實驗值進行對比,研究結果表明:改進的核函數可有效抑制模擬過程中壓力求解的振蕩現象; 核函數與對應粒子數密度比值曲線的形狀特征可真實反映粒子間相互作用關系,在穩定性分析中起著至關重要的作用。當核函數是光滑單調遞減非負函數且最大值為有限值、兩粒子間距離與影響半徑的比r/re在[0,1]區間時,曲線兩端附近核函數數值變化平緩更有利于使粒子保持合理距離,壓力求解更加穩定; 在r/re為0.8的附近,核函數值過小時會影響系統的動力學性能。
      As a particle-based method, moving particle semi-implicit method(MPS)is widely used for analyzing unsteady flow with free surface.However, a certain degree of pressure fluctuation may occur when solving a specific problem.In this paper, the influence of the shape feature of the kernel function curve on the stability of pressure solution in MPS is analyzed.An exponential polynomial kernel function is constructed, which is verified by a typical static pressure example(hydrostatic pressure problem)and a dynamic pressure example(liquid sloshing problem).Simulation is conducted and the results are compared with the theoretical solution or experimental results.It is found that the improved kernel function can effectively suppress the pressure oscillation in the simulation process.Studies have shown that the shape features of the ratio of the kernel function to the corresponding particle number density can truly reflect the interaction between particles and play a vital role in the analysis of pressure stability.When the improved kernel function is a smooth monotone decreasing non-negative function and its maximum value is a finite value and the value of r/re is in the range of [0, 1], gentle change of the numerical values of the kernel function is more conducive to keeping the particle spacing at a reasonable distance, and the pressure solution is more stable.In addition, the value of kernel function near r/re=0.8 cannot be too small, otherwise the dynamic performance of the system will be affected.


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      收稿日期: 2019-02-15。作者簡介: 張凱(1990—),男,博士生; 孫中國(通信作者),男,副教授;痦椖: 國家自然科學基金資助項目(51576154); 中央高;究蒲袠I務費專項資金資助項目(xjj2017114)。
      更新日期/Last Update: 2019-09-04