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