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Particle-Based non-Newtonian Fluid Animation for Melting Objects

Particle-Based non-Newtonian Fluid Animation for Melting Objects. Afonso Paiva Fabiano P. do Carmo Thomas Lewiner Geovan Tavares Matmidia - Departament of Mathematics – PUC-Rio. Fluid for Animation. Melt and Flow. Visually Realistic Computer Animations for Melting Objects.

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Particle-Based non-Newtonian Fluid Animation for Melting Objects

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  1. Particle-Based non-Newtonian Fluid Animation for Melting Objects Afonso Paiva Fabiano P. do Carmo Thomas Lewiner Geovan Tavares Matmidia - Departament of Mathematics – PUC-Rio

  2. Fluid for Animation

  3. Melt and Flow Visually Realistic Computer Animations for Melting Objects

  4. Overview • Related Works • Governing Equations • Viscoplastic Model • Solid-Liquid Transition • SPH Basics • Implementation • Tracking Free Surface • Results

  5. Related Works Grid-based Carlson et al., 2002 Particle-based Keiser et al., 2005

  6. Smoothed Particle Hydrodynamics - SPH Gingold & Monaghan (1977) and Lucy (1977) Popular in astrophysics because: • Resolution automatically adapts to density • Easy to combine with N-Body algorithms • Modeling compressible fluids • Can be extend to incompressible fluids

  7. Continuity Equation Momentum Equation Lagrangian Formulation of Navier-Stokes Equations • PDE → ODEs • Particle Methods to perform CFD • SPH, PIC, MAC, MPS, …

  8. Viscoplastic Model • P. R. S. Mendes, E. S. S. Dutra, J. R. R. Siffert, and M. F. Naccache. “Gas displacement of viscoplastic liquids in cappilary tubes” - Journal of Non-Newtonian Fluid Mechanics, 2005. • Based on Generalized Newtonian Liquid model • Stress Tensor:

  9. Viscoplastic Model Viscosity Function • n – power-law index • J – jump number: • yield stress • low shear rate viscosity • consistency index

  10. NS Equations Temperature > Fusion Point Liquid Temperature Jump Number Viscosity linearly Solid-Liquid Transition Heat Equation Viscosity Function

  11. Solid-Liquid Transition

  12. Overview • Related Works • Governing Equations • Viscoplastic Model • Solid-Liquid Transition • SPH Basics • Implementation • Tracking Free Surface • Results

  13. Quintic Spline SPH Basics Meshless Method • Particles are moving interpolation centers for fluid quantities • Easy to track fluid free surface SPH Average Operator

  14. SPH Gradient • Scalar • Vector • Divergent

  15. SPH Density SPH Approximation of Continuity Equation

  16. SPH Momentum Equation Pressure Equation of state • we can approximate the incompressible fluid by a quasi-compressible fluid (Batchelor, 1974)

  17. SPH Momentum Equation Stress Tensor

  18. SPH Laplacian • Traditionally in CG: • Inspired in SPH Projection Method (Cummins and Rudman, 1999)

  19. Implementation Leap-Frog Scheme Numerical Stability • Artificial Viscosity • XSPH • CFL Condition: Tree Search Method • Complexity:

  20. Rendering the Free Surface SPH Characteristic Function Topological Marching Cubes • T. Lewiner, H. Lopes, A. W. Vieira e G. Tavares. “Efficient implementation of marching cubes with topological guarantees” - JGT, 2003

  21. Rendering the Free Surface

  22. Work in Progress • Phase Transition→ Multiphase Flow • Rendering the Free Surface → Free Surface Tracking • Octree Particle Search → Pair-List

  23. That’s all Folks http://www.mat.puc-rio.br/~apneto

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