修正压力梯度粒子近似SPH方法计算大密度比界面流动  

Modified Particle Approximation to Pressure Gradients in the SPH Algorithm for Interfacial Flows With High Density Ratios

作　　者：徐丞君 徐胜利[2] 刘庆源 XU Chengjun;XU Shengli;LIU Qingyuan(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230025,P.R.China;School of Aerospace Engineering,Tsinghua University,Beijing 100084,P.R.China)

机构地区：[1]中国科学技术大学数学科学学院,合肥230026 [2]清华大学航天航空学院,北京100084

出　　处：《应用数学和力学》2019年第1期20-35,共16页Applied Mathematics and Mechanics

基　　金：中国运载火箭技术研究院基金(CALT201601);清华大学自主课题(20161080102)对本文的资助

摘　　要：计算了高密度比的多界面流动问题.为保证多相SPH(smoothed-particle hydrodynamics)方法捕捉界面光滑性和消除界面附近压力震荡,修正了动量方程压强梯度项的粒子近似,在界面施加了排斥力.采用Rayleigh-Taylor界面不稳定性、非Boussinesq锁定交换、溃坝和气泡上升等算例验证了该方法的准确性和健壮性,得到不同时刻界面(粒子)分布、压力云图和指定点压力时间分布、界面锋面距离等.所得结果表明:计算结果(如界面形状、光滑性和指定点压力分布等)与实验值或其他文献结果符合较好.修正的压力梯度项粒子近似,改善了多相SPH方法对高密度比、大变形和破碎多相界面的模拟能力和光滑性,同时界面附近未出现明显的压力震荡.Interfacial flows with high density ratios ranging from 1 to 1 000 were numerically investigated.Modified particle approximation was proposed for the pressure gradient term in the momentum equation and the repulsive force was imposed for virtual particles outside the interfaces. The R ayleigh-Taylor instability,non-Boussinesq lock exchange,dam-break flowand bubble buoyancy were numerically tested for validation of accuracy and robustness of the new SPH algorithm for multi-fluid flows. The particle distributions,pressure contours and pressure-time distributions at specified points were obtained from the computations. The results are in good agreement with those from references and experimental measurements.T he captured interfaces are more smooth in comparison with those from previous literatures and no obvious oscillations are observed in the vicinity of the interfaces.

关 键 词：SPH方法 多相流 Rayleigh-Taylor界面不稳定 溃坝 气泡 

分 类 号：O242.1[理学—计算数学]