Porous Flow in Particle-Based Fluid Simulations
Download
Report
Transcript Porous Flow in Particle-Based Fluid Simulations
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