对流传热问题的粒子-网格混合方法数值模拟
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摘要
移动粒子半隐式(MPS)方法是一种完全基于拉格朗日体系的粒子法,应用于不可压缩流体。MPS方法在描述存在大变形和相变的问题时具有很大的优势。然而当MPS方法中的Laplace模型应用于求解能量方程时会存在求解不精确的情况。本文在MPS方法的基础上,提出了一种粒子-网格混合求解方法。通过MPS方法求解动量守恒方程,耦合有限体积法(FVM)求解能量守恒方程,以达到对对流传热问题的精确求解。对一维导热问题进行了方法验证,证明了粒子-网格混合方法求解导热的有效性,并有较高的求解精度。利用粒子-网格混合方法模拟了方腔内的自然对流,结果表明,基于MPS方法和FVM的耦合方法可用于求解对流传热问题。
The moving particle semi-implicit(MPS) method, which is a particle method without grid meshes, is a full Lagrangian method for incompressible flows. It has advantages in describing fluid interface with large deformation and phase transition problems. However, when the Laplace model of MPS method is applied to solve the energy equation, there will be an inaccurate solution. In this paper, a particle-grid hybrid method was proposed based on MPS method. The momentum conservation equation was solved by MPS method and the energy conservation equation was solved by finite volume method(FVM) in the calculation so that the convective heat transfer problems could be solved by the particle-grid hybrid method. It is proved that the particle-grid hybrid method is effective and has high precision to solve the one-dimensional heat conduction problem. The particle-grid hybrid method was used to simulate the natural convection in the cavity. The results show that the coupling method based on MPS method and FVM can be used to solve the convective heat transfer problem.
The moving particle semi-implicit(MPS) method, which is a particle method without grid meshes, is a full Lagrangian method for incompressible flows. It has advantages in describing fluid interface with large deformation and phase transition problems. However, when the Laplace model of MPS method is applied to solve the energy equation, there will be an inaccurate solution. In this paper, a particle-grid hybrid method was proposed based on MPS method. The momentum conservation equation was solved by MPS method and the energy conservation equation was solved by finite volume method(FVM) in the calculation so that the convective heat transfer problems could be solved by the particle-grid hybrid method. It is proved that the particle-grid hybrid method is effective and has high precision to solve the one-dimensional heat conduction problem. The particle-grid hybrid method was used to simulate the natural convection in the cavity. The results show that the coupling method based on MPS method and FVM can be used to solve the convective heat transfer problem.
引文
[1] 项利峰.基于无网格算法的移动粒子半隐式方法研究及应用[D].西安:西安交通大学,2007.
[2] KOSHIZUKA S,OKA Y.Moving-particle semi-implicit method for fragmentation of incompressible fluid[J].Nuclear Science and Engineering,1996,123(3):421-434.
[3] MEIBURG E.Comparison of the molecular dynamics method and the direct simulation Monte Carlo technique for flows around simple geometries[J].The Physics of Fluids,1986,29(10):3 107-3 113.
[4] BIRD G.Direct simulation of high-vorticity gas flows[J].The Physics of Fluids,1987,30(2):364-366.
[5] GINGOLD R A,MONAGHAN J J.Smoothed particle hydrodynamics:Theory and application to non-spherical stars[J].Monthly Notices of the Royal Astronomical Society,1977,181(3):375-389.
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[7] GUO L,KAWANO Y,ZHANG S,et al.Numerical simulation of rheological behavior in melting metal using finite volume particle method[J].Journal of Nuclear Science and Technology,2010,47(11):1 011-1 022.
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[9] 刘虎,强洪夫,陈福振,等.一种新型光滑粒子动力学固壁边界施加模型[J].物理学报,2015,64(9):094701.LIU Hu,QIANG Hongfu,CHEN Fuzhen,et al.A new boundary treatment method in smoothed particle hydrodynamics[J].Acta Physica Sinica,2015,64(9):094701(in Chinese).
[10] 韩亚伟,强洪夫,赵玖玲,等.光滑粒子流体动力学方法固壁处理的一种新型排斥力模型[J].物理学报,2013,62(4):044702.HAN Yawei,QIANG Hongfu,ZHAO Jiuling,et al.A new repulsive model for solid boundary condition in smoothed particle hydrodynamics[J].Acta Physica Sinica,2013,62(4):044702(in Chinese).
[11] 周学君,陈丁,唐轶.一种新型SPH固壁边界处理的排斥力模型[J].长江科学院院报,2017,34(7):54-59.ZHOU Xuejun,CHEN Ding,TANG Yi.A repulsive model for solid boundary treatment in smoothed particle hydrodynamics[J].Journal of Yangtze River Sientific Research Institute,2017,34(7):54-59(in Chinese).
[12] 周学君,陈丁,黄文雄.基于长程力的SPH方法固壁边界处理[J].河海大学学报:自然科学版,2017,45(2):153-160.ZHOU Xuejun,CHEN Ding,HUANG Wen-xiong.Solid boundary treatment for SPH method based on long-range force[J].Journal of Hohai University:Natural Sciences,2017,45(2):153-160(in Chinese).
[13] 张锁春.光滑质点流体动力学(SPH)方法[J].计算物理,1996,13(4):385-397.ZHANG Suochun.Smoothed particle hydrodynamics (SPH) method[J].Chinese Journal of Computational Physics,1996,13(4):385-397(in Chinese).
[14] 朱晓临,汪欢欢,殷竞存.SPH流固耦合模拟自适应采样固壁虚粒子边界处理方法[J].图学学报,2018,39(3):381-388.ZHU Xiaolin,WANG Huanhuan,YIN Jingcun.Adaptive sampling method for solid wall virtual particle boundary handling in SPH fluid solid coupling simulation[J].Journal of Graphics,2018,39(3):381-388(in Chinese).
[15] 汤文辉,毛益明.SPH数值模拟中固壁边界的一种处理方法[J].国防科技大学学报,2001,23(6):54-57.TANG Wenhui,MAO Yiming.A method of processing rigid boundary condition in SPH simulation[J].Journal of National University of Defense Technology,2001,23(6):54-57(in Chinese).
[16] de VAHL D G.Natural convection of air in a square cavity:A bench mark numerical solution[J].International Journal for Numerical Methods in Fluids,1983,3(3):249-264.
[2] KOSHIZUKA S,OKA Y.Moving-particle semi-implicit method for fragmentation of incompressible fluid[J].Nuclear Science and Engineering,1996,123(3):421-434.
[3] MEIBURG E.Comparison of the molecular dynamics method and the direct simulation Monte Carlo technique for flows around simple geometries[J].The Physics of Fluids,1986,29(10):3 107-3 113.
[4] BIRD G.Direct simulation of high-vorticity gas flows[J].The Physics of Fluids,1987,30(2):364-366.
[5] GINGOLD R A,MONAGHAN J J.Smoothed particle hydrodynamics:Theory and application to non-spherical stars[J].Monthly Notices of the Royal Astronomical Society,1977,181(3):375-389.
[6] HEO S,KOSHIZUKA S,OKA Y.Numerical analysis of boiling on high heat-flux and high subcooling condition using MPS-MAFL[J].International Journal of Heat and Mass Transfer,2002,45(13):2 633-2 642.
[7] GUO L,KAWANO Y,ZHANG S,et al.Numerical simulation of rheological behavior in melting metal using finite volume particle method[J].Journal of Nuclear Science and Technology,2010,47(11):1 011-1 022.
[8] 刘玉侠,王裴.光滑粒子流体动力学的格式修正与界面处理方法[C]//全国流体力学学术会议论文集.[出版地不详]:[出版者不详],2012.
[9] 刘虎,强洪夫,陈福振,等.一种新型光滑粒子动力学固壁边界施加模型[J].物理学报,2015,64(9):094701.LIU Hu,QIANG Hongfu,CHEN Fuzhen,et al.A new boundary treatment method in smoothed particle hydrodynamics[J].Acta Physica Sinica,2015,64(9):094701(in Chinese).
[10] 韩亚伟,强洪夫,赵玖玲,等.光滑粒子流体动力学方法固壁处理的一种新型排斥力模型[J].物理学报,2013,62(4):044702.HAN Yawei,QIANG Hongfu,ZHAO Jiuling,et al.A new repulsive model for solid boundary condition in smoothed particle hydrodynamics[J].Acta Physica Sinica,2013,62(4):044702(in Chinese).
[11] 周学君,陈丁,唐轶.一种新型SPH固壁边界处理的排斥力模型[J].长江科学院院报,2017,34(7):54-59.ZHOU Xuejun,CHEN Ding,TANG Yi.A repulsive model for solid boundary treatment in smoothed particle hydrodynamics[J].Journal of Yangtze River Sientific Research Institute,2017,34(7):54-59(in Chinese).
[12] 周学君,陈丁,黄文雄.基于长程力的SPH方法固壁边界处理[J].河海大学学报:自然科学版,2017,45(2):153-160.ZHOU Xuejun,CHEN Ding,HUANG Wen-xiong.Solid boundary treatment for SPH method based on long-range force[J].Journal of Hohai University:Natural Sciences,2017,45(2):153-160(in Chinese).
[13] 张锁春.光滑质点流体动力学(SPH)方法[J].计算物理,1996,13(4):385-397.ZHANG Suochun.Smoothed particle hydrodynamics (SPH) method[J].Chinese Journal of Computational Physics,1996,13(4):385-397(in Chinese).
[14] 朱晓临,汪欢欢,殷竞存.SPH流固耦合模拟自适应采样固壁虚粒子边界处理方法[J].图学学报,2018,39(3):381-388.ZHU Xiaolin,WANG Huanhuan,YIN Jingcun.Adaptive sampling method for solid wall virtual particle boundary handling in SPH fluid solid coupling simulation[J].Journal of Graphics,2018,39(3):381-388(in Chinese).
[15] 汤文辉,毛益明.SPH数值模拟中固壁边界的一种处理方法[J].国防科技大学学报,2001,23(6):54-57.TANG Wenhui,MAO Yiming.A method of processing rigid boundary condition in SPH simulation[J].Journal of National University of Defense Technology,2001,23(6):54-57(in Chinese).
[16] de VAHL D G.Natural convection of air in a square cavity:A bench mark numerical solution[J].International Journal for Numerical Methods in Fluids,1983,3(3):249-264.