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 Darcy
2) Smoothed Particle Hydrodynamics (SPH)
Goal:
1) Macroscopic scale simulation
2) the changing behavior of the wet material
3) Full two-way coupling

Two popular ways to do fluid simulation:
1) Eulerian model
2) Lagrangian model

Smoothed Particle Hydrodynamics (SPH)
1) Highly deformable models
2) Interactive fluid simulation [Müller et al 2003 and
2005]

Flow through porous media using SPH
1) pore scale
Computational Expensive

the Law of Darcy
1) Discharge rate:
2) Darcy flux:
q
Q 
K

 KA ( Pb  Pa )

L
( P   g )
3) Pore water velocity:
v
q


K

( P   g )


Interpolation method
Smoothing kernel
Ex: Radially symmetric normalized kernel,
W poly 6 ( r , h ) 

315
64  h
(h  r )
2
9
2
3
0 r  h
 W ( r ) dr
1
Derivates of field quantities
(gradient/Laplacian) only affect the smoothing
kernel.

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
A( x) 
V
j
j
A j  W ( x j  xi , h j )

Two types of pressure gradients:
1) Capillary pressure gradient:
 Pi 
c
 V j P j  W ( x j  x i , h j ),
Pi  k (1  S i )
c
c
c

j
2) Pore pressure gradient:
 Pi 
p
V
j

P j  W ( x j  x i , h j ),
p
j
Pi
Pore water velocity:
v pi  
Ki
 i
p
   s 

p
 k S i   is   1 
 

0 



(  Pi   Pi   g )
p
c

Fluid diffusion inside the medium:
1) Eulerian approach
2) Quantity to be diffused: Fluid mass
3) Depend on the pore velocity, the particle
position, and the saturation.
 m pi
t

d
V m pj  W ( x j  x i , h j )
ij j
2
j
m pi  m pi   t
 m pi
t
,
d ij  v pj 
x j  xi
x j  xi

Sj

Density for a soaked object:
 oi   0  S i i  0
fluid

Stress reduction due to the fluid:
i
eff
  i  k Si I
p


Absorption: Fluid particle near the boundary > Fully saturated porous particle.
Emission:
1) Fluid particle near the boundary -> 0saturated porous particle
2) 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