1. Geometry Group Summer 08 Series Toon Lenaerts, Bart Adams, and Philip Dutre Presented by Michael Su May. 27.2008

2.  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

3.  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

4.  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

5.  the Law of Darcy 1) Discharge rate: 2) Darcy flux: 3) Pore water velocity:

6.  Interpolation method  Smoothing kernel Ex: Radially symmetric normalized kernel,  Derivates of field quantities (gradient/Laplacian) only affect the smoothing kernel.

7.  Porous Particle P i 1) Discrete properties: x i (Position), m i (Unsaturated mass), V i (Volume), ρ i (Material density), h i (Smoothing length), φ i (Porosity), K i (Permeability), and S i (Saturation). 2) Continuous properties: Interaction forces

8.  Two types of pressure gradients: 1) Capillary pressure gradient:, 2) Pore pressure gradient:,  Pore water velocity:

9.  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.,

10.  Density for a soaked object:  Stress reduction due to the fluid:

11.  Absorption: Fluid particle near the boundary - > Fully saturated porous particle.  Emission: 1) Fluid particle near the boundary -> 0- saturated porous particle 2) Dynamic fluid particle creation

12. Low Pore Pressure, High Permeability High Pore Pressure Low Permeability High Capillary Pressure

13.  Surface Tension Force  Adhesion forces  Friction forces  20,000 particles for the cloth  25,000 particles for the fluid

14.  30,000 porous particles for the armadillo  Small simulation time step to avoid penetrations