Robust Simulation of Sparsely Sampled Thin Features in SPH-Based Free Surface Flows

Transcription

1 Copyright of figures and other materials in the paper belong to original authors. Robust Simulation of Sparsely Sampled Thin Features in SPH-Based Free Surface Flows Xiaowei He et al. ACM SIGGRAPH 2015 Presented by Man-Ki Hong

2 Introduction SPH(Smoothed Particle Hydrodynamics) Useful method to simulate fluids Limitation : Sparsely sampled thin feature Lack of particles We propose following contribution to robustly simulate sparsely sampled thin features Surface Force Surface tension Air pressure Numerical Instability Two-scale pressure estimation Geometry-aware anisotropic filtering Man-Ki Hong # 2

3 Related Work Physics-Inspired Topology Changes for Thin Fluid Features [Chris wojtan et al./ ACM SIGGRAPH 2010] Mesh-based surface tracking method for thin features Preserving Fluid Sheets with Adaptively Sampled Anisotropic Particles [Ryoichi Ando et al./ TVCG 2012] Particle-based model for preserving fluid sheets of animated liquids Man-Ki Hong # 3

4 Related Work Ghost SPH for Animating Water [Hagit Schechter et al./ ACM SIGGRAPH 2012] New particle sampling algorithm to create a narrow layer of ghost particles Reconstructing Surfaces of Particle-Based Fluids Using Anisotropic Kernels [Jihun Yu et al./ ACM SIGGRAPH 2010] Formulate the implicit function as a sum of anisotropic smoothing kernels Man-Ki Hong # 4

5 Surface Forces Previous surface force method Continuum Surface Force(CSF) Particle-Based Fluid Simulation for Interactive Applications [Matthias Müller et al./ ACM SIGGRAPH 2003] Inter-particle Interaction Force(IIF) Weakly compressible SPH for free surface flows [Markus Becker et al./ ACM SIGGRAPH 2007] CSF method IIF method Man-Ki Hong # 5

6 Surface Forces Surface energy in a diffuse interface Free energy of a nonuniform system. I. Interfacial free energy [J. Cahn and J. Hilliard, 1958] V liquid volume κ squared gradient energy coefficient f c bulk free energy density c condensation field (known as color field) Man-Ki Hong # 6

7 Surface Forces Surface Tension Force Then we can take the surface free energy density term : Gradient of the color field : we can get energy density of each particle : ε i s = Man-Ki Hong # 7

8 Surface Forces Surface Tension Force Surface tension force is defined : For momentum conservation : Surface tension force tries to minimize the surface tension energy density Man-Ki Hong # 8

9 Surface Forces Surface Tension Force Man-Ki Hong # 9

10 Surface Forces Air Pressure Force Consider virtual air particle k j Man-Ki Hong # 10

11 Surface Forces Air Pressure Force Man-Ki Hong # 11

12 Surface Forces Air Pressure Force Compared with ghost SPH method Does not need air particles Does not require cost in calculating air pressure force Man-Ki Hong # 12

13 Numerical Instability Attraction Force Also called tensile instability Repulsion Force Occurs on thin features only Man-Ki Hong # 13

14 Numerical Instability Two-Scale Pressure Estimation To solve these instability problem, we use two different core radius in kernel function : α r/r 3 in 3D, r/r 2 in 2D m particle mass R radius of large kernel (R = 2.5d) r radius of small kernel (r = d) d expected reference distance between two particles And we use LPSPH method to convert each densities into pressures. Local Poisson SPH For Viscous Incompressible Fluids [Xiaowei He et al./ EUROGRAPHICS 2012] Man-Ki Hong # 14

15 Numerical Instability Two-Scale Pressure Estimation P i R is more accurate for particles in water bodies. But it is underestimated for particles on thin features. P i r does not have underestimation issue on thin features. Internal pressure at particle i (γ 0 ~ 0.5) β considers a balance between surface tension and thin features Smoothing radius parameters Man-Ki Hong # 15

16 Numerical Instability Anisotropic Pressure Filtering Inspired by surface reconstruction method Reconstructing Surfaces of Particle-Based Fluids Using Anisotropic Kernels [Jihun Yu et al./ ACM SIGGRAPH 2010] Anisotropic covariance matrix defined at particle i : Man-Ki Hong # 16

17 Numerical Instability Anisotropic Pressure Filtering Then we propose a tensor matrix T i Particles in water bodies, T i get closer to identity matrix. For particles on thin features, p i > p i R and T i becomes more anisotropic. Internal pressure force : Man-Ki Hong # 17

18 Numerical Instability Anisotropic Pressure Filtering Man-Ki Hong # 18

19 Results Implementation Local Poisson SPH solver Parallel index sorting algorithm Level-set approach for liquid surface reconstruction Setting quad-core Intel Xeon W GHz workstation 6GB memory Time step Δt = 0.001s Man-Ki Hong # 19

20 Results t s average computational time for surface forces t p average computational time for internal pressures t tot total computational time Man-Ki Hong # 20

21 Conclusion We identified two main factors affecting sparsely sampled thin features in SPH-based free surface flows : Surface forces Free surface energy functional in formulating surface tension force Handling air pressure effects without using air particles Numerical instability Nobel algorithm to calculate internal pressure forces on thin features Man-Ki Hong # 21

22 Conclusion Limitation Not as accurate as the ghost SPH method. Some parameters are not based on physics and so need to be tuned. Including κ and β The feature scale is limited by the resolution. Cannot handle thin features whose size are less then single particle. Surface reconstruction may destroy feature details. Man-Ki Hong # 22

23 Conclusion Future Work Compatibility with graphics hardware acceleration. Combining with the mesh-based tracking method. Animate complex liquid-solid interactions and air bubbles in large water bodies. Multiphase flow Man-Ki Hong # 23