Particle-Based non-Newtonian Fluid Animation for Melting Objects

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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
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Fluid for Animation
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Melt and Flow

• Visually Realistic Computer Animations for
  Melting Objects

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Overview

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

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

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Lagrangian Formulation of Navier-Stokes Equations

• PDE ? ODEs
• Particle Methods to perform CFD
• SPH, PIC, MAC, MPS,

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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

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Viscoplastic Model

• Viscosity Function
• n power-law index
• J jump number
• yield stress
• low shear rate viscosity
• consistency index

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Solid-Liquid Transition

• Heat Equation
• Viscosity Function

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Solid-Liquid Transition
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Overview

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

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SPH Basics

• Meshless Method
• Particles are moving interpolation centers for
  fluid quantities
• Easy to track fluid free surface
• SPH Average Operator

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SPH Gradient

• Scalar
• Vector
• Divergent

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SPH Density

• SPH Approximation of Density
• SPH Approximation of Continuity Equation

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SPH Density

• SPH Approximation of Continuity Equation

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SPH Momentum Equation

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

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SPH Momentum Equation

• Stress Tensor

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SPH Laplacian

• Traditionally in CG
• Inspired in SPH Projection Method (Cummins and
  Rudman, 1999)

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Implementation

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

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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

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Rendering the Free Surface
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Work in Progress

• Phase Transition ? Multiphase Flow
• Rendering the Free Surface ? Free Surface
  Tracking
• Octree Particle Search ? Pair-List

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Thats all Folks
http//www.mat.puc-rio.br/apneto