A meshless method based on moving least squares for the simulation of free surface flows

详细信息    查看全文

• 作者：Yu Lu ; An-kang Hu ; Ya-chong Liu ; Chao-shuai Han
• 关键词：Meshless method ; Moving least squares (MLS) ; Free surface flows ; Finite pointset method (FPM) ; Dam ; breaking flows ; Solitary wave propagation ; Liquid sloshing of tanks ; 无网格法 ; 移动最小二乘
自由面流动 有限点法 ; 溃坝流 孤立波传播 液舱晃荡 ; U661.1
• 刊名：Journal of Zhejiang University - Science A
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：17
• 期：2
• 页码：130-143
• 全文大小：3,843 KB
• 参考文献：Ata, R., Soulaïmani, A., 2005. A stabilized SPH method for inviscid shallow water flows. International Journal for Numerical Methods in Fluids, 47(2):139–159. http://​dx.​doi.​org/​10.​1002/​fld.​801CrossRef MathSciNet MATH
  Belytschko, T., Krongauz, Y., Fleming, M., et al., 1996. Smoothing and accelerated computations in the element free Galerkin method. Journal of Computational and Applied Mathematics, 74(1-2):111–126. http://​dx.​doi.​org/​10.​1016/​0377-0427(96)00020-9CrossRef MathSciNet MATH
  Benz, W., Asphaug, E., 1995. Simulations of brittle solids using smooth particle hydrodynamics. Computer Physics Communications, 87(1-2):253–265. http://​dx.​doi.​org/​10.​1016/​0010-4655(94)00176-3CrossRef MATH
  Chan, R.K.C., Street, R.L., 1970. A computer study of finiteamplitude water waves. Journal of Computational Physics, 6(1):68–94. http://​dx.​doi.​org/​10.​1016/​0021-9991(70)90005-7CrossRef MATH
  Chorin, A.J., 1968. Numerical solution of the Navier-Stokes equations. Mathematics of Computation, 22(104):745–762. http://​dx.​doi.​org/​10.​1090/​S0025-5718-1968-0242392-2CrossRef MathSciNet MATH
  Cleary, P.W., Monaghan, J.J., 1999. Conduction modelling using smoothed particle hydrodynamics. Journal of Computational Physics, 148(1):227–264. http://​dx.​doi.​org/​10.​1006/​jcph.​1998.​6118CrossRef MathSciNet MATH
  Cleary, P.W., Prakash, M., 2004. Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 362(1822):2003–2030. http://​dx.​doi.​org/​10.​1098/​rsta.​2004.​1428CrossRef MathSciNet MATH
  Cummins, S.J., Rudman, M., 1999. An SPH projection method. Journal of Computational Physics, 152(2):584–607. http://​dx.​doi.​org/​10.​1006/​jcph.​1999.​6246CrossRef MathSciNet MATH
  Deshpande, S.M., Kulkarni, P.S., Ghosh, A.K., 1998. New developments in kinetic schemes. Computers & Mathematics with Applications, 35(1-2):75–93. http://​dx.​doi.​org/​10.​1016/​S0898-1221(97)00259-9CrossRef MathSciNet MATH
  Dilts, G.A., 1999. Moving-least-squares-particle hydrodynamics— I. Consistency and stability. International Journal for Numerical Methods in Engineering, 44(8): 1115–1155. http://​dx.​doi.​org/​10.​1002/​(SICI)1097-0207 (19990320)44:8<1115::AID-NME547>3.0.CO;2-LCrossRef MathSciNet MATH
  Dumbser, M., 2013. A diffuse interface method for complex three-dimensional free surface flows. Computer Methods in Applied Mechanics and Engineering, 257:47–64. http://​dx.​doi.​org/​10.​1016/​j.​cma.​2013.​01.​006CrossRef MathSciNet MATH
  Ellero, M., Kröger, M., Hess, S., 2002. Viscoelastic flows studied by smoothed particle dynamics. Journal of Non-Newtonian Fluid Mechanics, 105(1):35–51. http://​dx.​doi.​org/​10.​1016/​S0377-0257(02)00059-9CrossRef MATH
  Fang, J., Owens, R.G., Tacher, L., et al., 2006. A numerical study of the SPH method for simulating transient viscoelastic free surface flows. Journal of Non-Newtonian Fluid Mechanics, 139(1-2):68–84. http://​dx.​doi.​org/​10.​1016/​j.​jnnfm.​2006.​07.​004CrossRef MATH
  Ferrari, A., Dumbser, M., Toro, E.F., et al., 2008. A new stable version of the SPH method in Lagrangian coordinates. Communications in Computational Physics, 4:378–404 (in Russian).MathSciNet
  Ferrari, A., Dumbser, M., Toro, E.F., et al., 2009. A new 3D parallel SPH scheme for free surface flows. Computers & Fluids, 38(6):1203–1217. http://​dx.​doi.​org/​10.​1016/​j.​compfluid.​2008.​11.​012CrossRef MathSciNet MATH
  Flebbe, O., Muenzel, S., Herold, H., et al., 1994. Smoothed particle hydrodynamics: physical viscosity and the simulation of accretion disks. The Astrophysical Journal, 431:754–760. http://​dx.​doi.​org/​10.​1086/​174526CrossRef
  Gingold, R.A., Monaghan, J.J., 1977. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181(3):375–389. http://​dx.​doi.​org/​10.​1093/​mnras/​181.​3.​375CrossRef MATH
  Kishev, Z.R., Hu, C., Kashiwagi, M., 2006. Numerical simulation of violent sloshing by a CIP-based method. Journal of Marine Science and Technology, 11(2):111–122. http://​dx.​doi.​org/​10.​1007/​s00773-006-0216-7CrossRef
  Koshizuka, S., Oka, Y., 1996. Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nuclear Science and Engineering, 123(3):421–434.
  Koshizuka, S., Oka, Y., Tamako, H., et al., 1995. A Particle Method for Calculating Splashing of Incompressible Viscous Fluid. Technical Report No. CONF-950420–TRN: 97:001160–0134, American Nuclear Society, Inc., La Grange Park, IL,USA.
  Libersky, L.D., Petschek, A.G., Carney, T.C., et al., 1993. High strain Lagrangian hydrodynamics a threedimensional SPH code for dynamic material response. Journal of Computational Physics, 109(1):67–75. http://​dx.​doi.​org/​10.​1006/​jcph.​1993.​1199CrossRef MATH
  Löhner, R., Sacco, C., Oñate, E., et al., 2002. A finite point method for compressible flow. International Journal for Numerical Methods in Engineering, 53(8):1765–1779. http://​dx.​doi.​org/​10.​1002/​nme.​334CrossRef MATH
  Lu, Y., Hu, A.K., Liu, Y.C., 2015. A finite pointset method for the numerical simulation of free surface flow around a ship. Journal of Marine Science and Technology, p.1–13. http://​dx.​doi.​org/​10.​1007/​s00773-015-0342-1
  Lucy, L.B., 1977. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82:1013–1024. http://​dx.​doi.​org/​10.​1086/​112164CrossRef
  Martin, J.C., Moyce, W.J., 1952. Part IV.An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 244(882):312–324. http://​dx.​doi.​org/​10.​1098/​rsta.​1952.​0006CrossRef MathSciNet
  Maveyraud, C., Benz, W., Sornette, A., et al., 1999. Solid friction at high sliding velocities: an explicit threedimensional dynamical smoothed particle hydrodynamics approach. Journal of Geophysical Research, 104(B12):28769–28788. http://​dx.​doi.​org/​10.​1029/​1999JB900217CrossRef
  Monaghan, J.J., 1994. Simulating free surface flows with SPH. Journal of Computational Physics, 110(2):399–406. http://​dx.​doi.​org/​10.​1006/​jcph.​1994.​1034CrossRef MATH
  Monaghan, J.J., 2002. SPH compressible turbulence. Monthly Notices of the Royal Astronomical Society, 335(3):843–852. http://​dx.​doi.​org/​10.​1046/​j.​1365-8711.​2002.​05678.​xCrossRef MathSciNet
  Monaghan, J.J., Kocharyan, A., 1995. SPH simulation of multi-phase flow. Computer Physics Communications, 87(1-2):225–235. http://​dx.​doi.​org/​10.​1016/​0010-4655(94)00174-ZCrossRef MATH
  Morris, J.P., 2000. Simulating surface tension with smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, 33(3):333–353. http://​dx.​doi.​org/​10.​1002/​1097-0363(20000615)33:3<33 3::AID-FLD11>3.0.CO;2-7CrossRef MATH
  Morris, J.P., Fox, P.J., Zhu, Y., 1997. Modeling low Reynolds number incompressible flows using SPH. Journal of Computational Physics, 136(1):214–226. http://​dx.​doi.​org/​10.​1006/​jcph.​1997.​5776CrossRef MATH
  Oger, L., Savage, S.B., 1999. Smoothed particle hydrodynamics for cohesive grains. Computer Methods in Applied Mechanics and Engineering, 180(1-2):169–183. http://​dx.​doi.​org/​10.​1016/​S0045-7825(99)00054-7CrossRef MATH
  Oñate, E., Idelsohn, S.R., 1998. A mesh-free finite point method for advective-diffusive transport and fluid flow problems. Computational Mechanics, 21(4-5):283–292. http://​dx.​doi.​org/​10.​1007/​s004660050304CrossRef MathSciNet MATH
  Oñate, E., Idelsohn, S.R., Zienkievicz, O.C., et al., 1996a. A finite point method in computational mechanics to convective transport and fluid flow. International Journal for Numerical Methods in Engineering, 39(22):3839–3866. http://​dx.​doi.​org/​10.​1002/​(SICI)1097-0207(19961130)39: 22<3839::AID-NME27>3.0.CO;2-RCrossRef MathSciNet MATH
  Oñate, E., Idelsohn, S.R., Zienkievicz, O.C., et al., 1996b. A stabilized finite point method for analysis of fluid mechanics problems. Computer Methods in Applied Mechanics and Engineering, 139(1-4):315–346. http://​dx.​doi.​org/​10.​1016/​S0045-7825(96)01088-2CrossRef MathSciNet MATH
  Oñate, E., Sacco, C., Idelsohn, S.R., 2000. A finite point method for incompressible flow problems. Computing and Visualization in Science, 3(1-2):67–75. http://​dx.​doi.​org/​10.​1007/​s007910050053CrossRef MATH
  Shao, S., Lo, E.Y., 2003. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Advances in Water Resources, 26(7):787–800. http://​dx.​doi.​org/​10.​1016/​S0309-1708(03)00030-7CrossRef
  Song, C., Zhang, H.X., Huang, J., et al., 2006. Meshless simulation for skeleton driven elastic deformation. Journal of Zhejiang University-SCIENCE A, 7(9):1596–1602. http://​dx.​doi.​org/​10.​1631/​jzus.​2006.​A1596CrossRef MATH
  Takeda, H., Miyama, S.M., Sekiya, M., 1994. Numerical simulation of viscous flow by smoothed particle hydrodynamics. Progress of Theoretical Physics, 92(5):939–960. http://​dx.​doi.​org/​10.​1143/​ptp/​92.​5.​939CrossRef
  van der Vorst, H.A., 1981. Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems. Journal of Computational Physics, 44(1):1–19. http://​dx.​doi.​org/​10.​1016/​0021-9991(81)90034-6CrossRef MathSciNet MATH
  van der Vorst, H.A., 1992. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 13(2):631–644. http://​dx.​doi.​org/​10.​1137/​0913035CrossRef MATH
  Watkins, S.J., Bhattal, A.S., Francis, N., et al., 1996. A new prescription for viscosity in smoothed particle hydrodynamics. Astronomy and Astrophysics Supplement Series, 119(1):177–187. http://​dx.​doi.​org/​10.​1051/​aas:1996104CrossRef
  
• 作者单位：Yu Lu (1)
  An-kang Hu (1) (2)
  Ya-chong Liu (1)
  Chao-shuai Han (1)
  
  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China
  2. CIMC Ocean Engineering Design & Research Institute Co., Ltd., Shanghai, 201206, China
  
• 刊物类别：Engineering
• 刊物主题：Physics
  Mechanics, Fluids and Thermodynamics
  Chinese Library of Science
  
• 出版者：Zhejiang University Press, co-published with Springer
• ISSN：1862-1775

文摘

In this paper, a meshless method based on moving least squares (MLS) is presented to simulate free surface flows. It is a Lagrangian particle scheme wherein the fluid domain is discretized by a finite number of particles or pointset; therefore, this meshless technique is also called the finite pointset method (FPM). FPM is a numerical approach to solving the incompressible Navier–Stokes equations by applying the projection method. The spatial derivatives appearing in the governing equations of fluid flow are obtained using MLS approximants. The pressure Poisson equation with Neumann boundary condition is handled by an iterative scheme known as the stabilized bi-conjugate gradient method. Three types of benchmark numerical tests, namely, dam-breaking flows, solitary wave propagation, and liquid sloshing of tanks, are adopted to test the accuracy and performance of the proposed meshless approach. The results show that the FPM based on MLS is able to simulate complex free surface flows more efficiently and accurately. Keywords Meshless method Moving least squares (MLS) Free surface flows Finite pointset method (FPM) Dam-breaking flows Solitary wave propagation Liquid sloshing of tanks