Particle-Based non-Newtonian Fluid Animation for Melting Objects - PowerPoint PPT Presentation

1 / 24
About This Presentation
Title:

Particle-Based non-Newtonian Fluid Animation for Melting Objects

Description:

... Implementation Leap-Frog Scheme Numerical Stability Artificial ... Melt and Flow Overview Related Works Smoothed Particle Hydrodynamics ... – PowerPoint PPT presentation

Number of Views:127
Avg rating:3.0/5.0
Slides: 25
Provided by: AfonsoPa
Category:

less

Transcript and Presenter's Notes

Title: Particle-Based non-Newtonian Fluid Animation for Melting Objects


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
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
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
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 Density
  • SPH Approximation of Continuity Equation

16
SPH Density
  • SPH Approximation of Continuity Equation

17
SPH Momentum Equation
  • Pressure
  • Equation of state
  • we can approximate the incompressible fluid by a
    quasi-compressible fluid (Batchelor, 1974)

18
SPH Momentum Equation
  • Stress Tensor

19
SPH Laplacian
  • Traditionally in CG
  • Inspired in SPH Projection Method (Cummins and
    Rudman, 1999)

20
Implementation
  • Leap-Frog Scheme
  • Numerical Stability
  • Artificial Viscosity
  • XSPH
  • CFL Condition
  • Tree Search Method
  • Complexity

21
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

22
Rendering the Free Surface
23
(No Transcript)
24
Work in Progress
  • Phase Transition ? Multiphase Flow
  • Rendering the Free Surface ? Free Surface
    Tracking
  • Octree Particle Search ? Pair-List

25
Thats all Folks
http//www.mat.puc-rio.br/apneto
Write a Comment
User Comments (0)
About PowerShow.com