geometry group summer 08 series toon lenaerts, bart adams, and philip dutre presented by michael su...
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Geometry Group Summer 08 Series
Toon Lenaerts, Bart Adams, and Philip Dutre
Presented by Michael Su
May. 27.2008
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Introduction Previous Work Review – Physics background Review – Smoothed Particle
Hydrodynamics Modeling Porous Materials Simulating Porous Flow Changing Material Properties Porous Medium-Fluid Coupling Result & Discussion
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Problem: Fluid-Penetrable object simulation Approach:
1) the Law of Darcy2) Smoothed Particle Hydrodynamics (SPH)
Goal:1) Macroscopic scale simulation2) the changing behavior of the wet material3) Full two-way coupling
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Two popular ways to do fluid simulation:1) Eulerian model2) Lagrangian model
Smoothed Particle Hydrodynamics (SPH)1) Highly deformable models2) Interactive fluid simulation [Müller et al 2003 and 2005]
Flow through porous media using SPH1) pore scale Computational
Expensive
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the Law of Darcy1) Discharge rate:
2) Darcy flux:
3) Pore water velocity:
L
PPKAQ ab )(
)( gPK
q
)( gPKq
v
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Interpolation methodSmoothing kernel
Ex: Radially symmetric normalized kernel,
Derivates of field quantities(gradient/Laplacian) only affect the smoothing kernel.
32296 )(
64
315),( rh
hhrWpoly
hr 0
1)( drrW
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Porous Particle Pi
1) Discrete properties: xi (Position), mi(Unsaturated mass), Vi(Volume), ρi(Material density), hi (Smoothing length), φi(Porosity), Ki
(Permeability), and Si(Saturation).2) Continuous properties: Interaction forces
j
jijjj hxxWAVxA ),()(
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Two types of pressure gradients:
1) Capillary pressure gradient:
,
2) Pore pressure gradient:
,Pore water velocity:
)1( icc
i SkP
1
0
s
si
ipp
i SkP
j
jijcjj
ci hxxWPVP ),(
j
jijpjj
pi hxxWPVP ),(
)( gPPK
v ci
pi
i
ipi
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Fluid diffusion inside the medium:1) Eulerian approach2) Quantity to be diffused: Fluid mass3) Depend on the pore velocity, the
particle position, and the saturation.
,
),(2jij
jpjjij
pi hxxWmVdt
m
j
ij
ijpjij S
xx
xxvd
t
mtmm pi
pipi
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Density for a soaked object:
Stress reduction due to the fluid:
fluidiioi S 00
ISk ip
ieffi
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Absorption: Fluid particle near the boundary -> Fully saturated porous particle.
Emission: 1) Fluid particle near the boundary -> 0-saturated porous particle2) Dynamic fluid particle
creation
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Low Pore Pressure, High Permeability
High Pore Pressure
Low Permeability
High Capillary Pressure
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Surface Tension Force
Adhesion forces Friction forces 20,000 particles
for the cloth 25,000 particles
for the fluid
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30,000 porous particles for the armadillo Small simulation time step to avoid
penetrations
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