Geometry Group Summer 08 Series
Toon Lenaerts, Bart Adams, and Philip Dutre
Presented by Michael Su
May. 27.2008
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
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
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
the Law of Darcy1) Discharge rate:
2) Darcy flux:
3) Pore water velocity:
L
PPKAQ ab )(
)( gPK
q
)( gPKq
v
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
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 ),()(
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
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
Density for a soaked object:
Stress reduction due to the fluid:
fluidiioi S 00
ISk ip
ieffi
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
Low Pore Pressure, High Permeability
High Pore Pressure
Low Permeability
High Capillary Pressure
Surface Tension Force
Adhesion forces Friction forces 20,000 particles
for the cloth 25,000 particles
for the fluid
30,000 porous particles for the armadillo Small simulation time step to avoid
penetrations
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