A Hybrid Mesh-Grid
Approach for Efficient
Large Body Water
Simulation
Morten Bojsen-Hansen
Aarhus University
October 27, 2011
Question
• Beskriv din metode med særligt henblik pa
˚ de
elementer som adskiller den fra eksisterende
teknikker.
• Reflekter over dine metodevalg og eventuelle
alternativer hertil.
• Evaluer dine resultater.
What do we mean by grid and mesh?
Stable fluids and level set methods
fluid cells
Stable
Fluids
Level Set
Method
velocity field
... both grid-based.
Why not simply increase resolution?
Lentine et. al, SIGGRAPH 2010
Just increase resolution of surface!
• Goktekin et. al, SIGGRAPH 2004
• Bargteil et. al, ToG 2006
• Wojtan et. al, SIGGRAPH 2008
• Kim et. al, SIGGRAPH ASIA 2009
Method overview
Meshbased
physics
Gridbased
physics
Constructing the ghost mesh
Sample implicit surface
Reconstruct explicit surface
Constructing the ghost mesh
Sample implicit surface
Reconstruct explicit surface
Constructing the ghost mesh
Sample implicit surface
Reconstruct explicit surface
Method overview
Meshbased
physics
Gridbased
physics
Correspondence: projection
Correspondence: projection
Orthogonal or vertical projection
Correspondence: what to map
Method overview
Meshbased
physics
Gridbased
physics
Grid-based physics: model
Model: inviscid incompressible Euler equations
∂u
1
= − (u · ∇) u − ∇p + f
∂t
ρ
∇·u=0
Grid-based physics: model
Model: inviscid incompressible Euler equations
∂u
1
= − (u · ∇) u − ∇p + f
∂t
ρ
∇·u=0
u(n)
Advection
ua
Grid-based physics: model
Model: inviscid incompressible Euler equations
∂u
1
= − (u · ∇) u − ∇p + f
∂t
ρ
∇·u=0
u(n)
Advection
ua
External
forces
uf
Grid-based physics: model
Model: inviscid incompressible Euler equations
∂u
1
= − (u · ∇) u − ∇p + f
∂t
ρ
∇·u=0
u(n)
Advection
ua
External
forces
uf
Pressure
projection
p(n)
u(n+1)
Grid-based physics: pressure
Linear system for unknown pressure inside fluid
pi−1
pi
0
xi−1
xi
xi+1
pi−1
pi
pI = 0
pi θ−1
θ
xi−1
xi
xI
xi+1
Method overview
Meshbased
physics
Gridbased
physics
Mesh-based physics
∂ 2h
= gd∇2 h
2
∂t
(errata to thesis)
Mesh-based physics
• Hydrostatic pressure: p = ρgd
• Validity of assumptions
2
• Coupling: ∂∂t h2 = p∇2 h
• Reflecting boundary conditions
• Discretisation
Results
• Wave speed proportional to pressure (2D)
• Reflecting solid boundary condition (2D)
• Vertex weighting strategies (2D)
• Raindrops in pool of water (3D)
• Sphere hitting pool of water (3D)
• Performance
Future work
• Implicit solver
• Solid boundary conditions
• Particles
• Adaptive subdivision and interpolation
The end
Thanks! Questions?
Solid boundary condition
So far we’ve talked about the free-surface boundary
condition. What about the solid boundary?
Push vertex adjacent to wall in outward normal
direction with force proportional to pressure in the
grid cell containing vertex. Project vertex to
boundary if it enters wall.