Smoothed Particle Hydrodynamics (SPH).pptx

1、Smoothed Particle Hydrodynamics (SPH),Advanced Topic in Computer Graphics & Visualization Survey Presentation,Outline,Introduction Basic Ideas of SPH Advantages of SPH Applications,Smoothed Particle Hydrodynamics,2,Introduction,Grid-based numerical methods (FVM, FEM) have been widely applied to vari

2、ous areas of computational fluid dynamics and computational solid mechanics.,Smoothed Particle Hydrodynamics,3,Grid-based numerical methods suffer from difficulties in some aspects.,Introduction,Meshfree method can deal with the above problems,Smoothed Particle Hydrodynamics,4,One of the oldest mesh

3、free particle methods: Smoothed Particle Hydrodynamics (SPH),astrophysical problem,Basic Ideas of SPH,In SPH, the state of a system is represented by a set of distributed particles. Each particle has its own material property and interacts with others within the range controlled by a smoothing funct

4、ion,Smoothed Particle Hydrodynamics,5,Basic Ideas of SPH,SPH is a integral representation.,Smoothed Particle Hydrodynamics,6,Kernel Approximation,Basic Ideas of SPH,Then the computational domain is discretized by representing it with a set of particles.,Smoothed Particle Hydrodynamics,7,Particle App

5、roximation,Basic Ideas of SPH,Summary: The fluid is presented by a set of particles following the fluid motion. Each particle carries mass ,velocity and other properties. SPH formulation is directly based on the macroscopic governing equation of fluid flow .,Smoothed Particle Hydrodynamics,8,Advanta

6、ges of SPH,A particle-based method with Lagrangian nature. By proper distribution of the particles, the free surfaces can be traced naturally in the process of simulation. SPH is suitable to follow large surface deformation. SPH is extremely suitable for problems where the object under consideration

7、 is not a continuum. SPH is relatively easier in numerical implementation.,Smoothed Particle Hydrodynamics,9,Applications,Vast range of applications: high explosive detonation and explosion micro drop dynamics heat conduction fluid-solid interaction metal forming ,Smoothed Particle Hydrodynamics,10,

8、blood flow and vessel wall interaction,Applications,A particle-based method for interactive fluid simulation and rendering,Smoothed Particle Hydrodynamics,11,Pouring water into a glass,M. Muller, D. Charypar, M. Gross, Particle-based fluid simulation for interactive applications, Eurographics/ SIGGR

9、APH Symposium on Computer Animation 2003: 154-159, 2003.,Fluid with free surfaces Derive the viscosity and pressure force fields from the Navier-Stokes equation Design new special purpose smoothing function,Applications,Interaction of fluids with deformable solids,Smoothed Particle Hydrodynamics,12,

10、A box falls into a pool and generates a shock wave that causes the pool to fracture,M. Muller, S. Schirm, et al, “Interaction of fluids with deformable solids, Comp. Anim. Virtual Worlds 15: 159-171, 2004.,Particle-based fluids Mesh-based deformable solids Virtual boundary particles,References,J. J.

11、 Monaghan, Smoothed particle hydrodynamics, Rep. Prog. Phys. 68(2005): 1703-1759, 2005. L. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82, 10131024, 1977. R. Gingold, and J. J. Monaghan, Smoothed particle hydrodynamics - Theory and application to non-spherical sta

12、rs, MNRAS 181, 375389, 1977. M.B. Liu, G.R. Liu, K.Y. Lam, Constructing smoothing functions in smoothed particle hydrodynamics with applications, J Comput Appl Math 155(2): 263284, 2003. M. B. Liu, G. R. Liu, Smoothed particle hydrodynamics (SPH): an overview and recent developments, Arch Comput Met

13、hods Eng 17: 25-76, 2010. J. J. Monaghan, J. C. Lattanzio, A refined particle method for astrophysical problems, Astron Astrophys 149(1): 135-143, 1985. J. J. Monaghan, J. C. Lattanzio, A simulation of the collapse and fragmentation of cooling molecular clouds, Astrophys J 375(1): 177-189, 1991. M.

14、B. Liu, G. R. Liu, A one-dimensional meshfree particle formulation for simulating shock waves, Shock Waves 13(3): 201-211, 2003.,Smoothed Particle Hydrodynamics,13,References,H. S. Fang, K. Bao, J. A. Wei, et al, Simulations of droplet spreading and solidification using an improved SPH model, Numer

15、Heat Transfer A, Appl 55(2): 124-143, 2009. J. K. Chen, J. E. Beraun, T. C. Carney, A corrective smoothed particle method for boundary value problems in heat conduction, Int J Numer Methods Eng 46: 231-252, 1999. M. Muller, D. Charypar, M. Gross, Particle-based fluid simulation for interactive appli

16、cations, Eurographics/SIGGRAPH Symposium on Computer Animation 2003: 154-159, 2003. J. Bonet, S. Kulasegaram, Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations, Int J Numer Methods Eng 47(6): 1189-1214, 2000. R. C. Batra, G. M. Zhang

17、, Analysis of adiabatic shear bands in elasto-thermo-viscoplastic materials by modified smoothed-particle hydrodynamics (MSPH) method, Journal of Computational Physics 201: 172-190, 2004. A. Colagrossi, M. Landrini, Numerical simulation of interfacial flows by smoothed particle hydrodynamics, Journal of Computational Physics 191: 448-475, 2003. J. Qin, W. M. Pang, B. P. Nguyen, et al,