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Detail-Preserving Fluid Control
N. Thűrey
R. Keiser
M. Pauly
U. Rűde
SCA 2006
Abstract
◇ A new fluid control technique
- Scale-dependent force control
- Preserve small-scale fluid detail
◇ Control particles define local force fields
- A physical simulation
- A sequence of target shapes
◇ A multi-scale decomposition of the velocity field
◇ Small-scale detail is preserved
Introduction
◇ Realism of fluids is important
[CMT04]
◇ The fluid controlling for animation is also important
[SY05b]
◇ Fine-scale detail such as small eddies or drops
Introduction
◇ In previous method, control particles directly
influence the fluid velocity field
- It can cause noticeable smoothing effects
◇ To avoid this artificial viscosity,
- Decompose the velocity field into coarse- and fine scale
component
- Only apply control forces to the low-frequency part
- High-frequency components are largely unaffected
- small-scale detail and turbulence are better preserved
Introduction
◇ We achieve this decomposition by smoothing
the velocity field using a low-pass filter
◇ Velocity control forces are computed with respect to
the smoothed velocity field
◇ Scale-separated fluid control
- Much better preserved
- More dynamic and realistic looking simulations
Related Work
◇ Our control paradigm is based on the concept of
control particle, similar to [FF01]
◇ Control particles are independent of the underlying
fluid model
[FF01] A 3D Control Curve
Related Work
◇ [REN04] present a method for the directable animation
of photorealistic liquids using the particle levelset
◇ [TMPS03] presented an optimization technique to
solve for the control parameters
Related Work
◇ [FL04] proposed the idea of driving smoke toward
target smoke density
◇ [HK04] derive potential fields from the initial
distribution of smoke and target shape
Related Work
◇ smoke[SY05a] and liquids[SY05b] matched the level
set surface of the fluid with static or moving target shape
Fluid Simulation Models
◇ We use two fluid simulation models to demonstrate
our control method
◇ Smoothed Particle Hydrodynamics (SPH)
◇ The Lattice-Boltzmann Method (LBM)
Smoothed Particle Hydrodynamics (SPH)
◇ As(r) : interpolation value at location r by a weighted
sum of contributions from all particles
◇ j : iterates over all particles, mj : the mass of particle j
◇ rj : its postion, ρj : density of particle j
◇ Aj : the field quantity at rj
◇ W(r,h) : smoothing kernel with radius h
Smoothed Particle Hydrodynamics (SPH)
◇ Numerically solving the Navier-Stokes equations
The Lattice-Boltzmann Method (LBM)
◇ A grid based method
◇ Each grid cell stores a set of distribution functions
◇ The common three-dimensional LBM model D3Q19
The Lattice-Boltzmann Method (LBM)
Streaming
◇ Streaming  Collision  Relaxation
The Lattice-Boltzmann Method (LBM)
ei : nineteen grid velocitys(0~18) wi : w0=1/3, w1..6=1/18,w7..18=1/36
: physical fluid viscosity
Fluid Control
◇ Generating Control Particles
◇ Controlling fluid using attraction force and velocity
force
◇ Detail-Preserving Control
Generating Control Particles
◇ Motion given by precomputed function [FM97, FF01]
◇ Shape given by a Mesh [JSW05]
◇ Motion from another fluid simulation
- using SPH, LBM
- very coarse simulation
- The simulation may even run in realtime to animator
Control Forces
◇ Attraction force : Force that pulls fluid towards
the control particles
◇ Velocity Force : modifying the velocity of the fluid
according to the flow determined by the control particles
◇ Control Particle Variables
- pi : position of control particle
- vi : velocity of control particle
- hi : influence radius (2.5times the average distance)
Attraction Force
◇ This force is scaled down when the influence region
of the control particle is already covered with fluid
◇ Scale factor for attraction force
Attraction Force
◇ Attraction force on a fluid element e
◇
: global contant that defines the strength of the
attraction force
◇ if
is negative, it will result in a repulsive force
Velocity Force
◇ Velocity Force on a fluid element e
◇ v(e) : the velocity of the fluid element e
◇
: a constant that defines the influence of the
velocity force
Total Force
◇ Total control force fc(e) = fa(e) + fv(e)
◇ The new total force per volume f(e) = fc(e) + ff(e)
◇ ff(e) : the fluid force from the physical fluid simulation
Detail-Preserving Control
◇ The velocity force lead to an
averaging of the fluid velocities
◇ Undesirable artificial viscosity
◇ We want the natural smallscale fluid motion
Detail-Preserving Control
Detail-Preserving Control
Detail-Preserving Control
◇ Smoothed velocity field
◇ This smoothed version of the fluid velocity replaces
V(e) in Equation 7
Detail-Preserving Control
◇
◇
is low pass filtered velocity
is high pass filtered velocity
◇ vp is the interpolated velocity of the control particles at
a fluid element e
Results and Discussion
◇ We have implemented our control algorithm for both an
SPH and an LBM fluid solver
◇ Within the SPH solver, the existing acceleration
structures can be used to query fluid particles in the
neighborhood of a control particle
◇ For the LBM solver, control particles are rasterized to
the grid
Results and Discussion
◇ The simulation using LBM with a 3003 grid resolution took
142s per frame, including 4s for computing the control force
◇ These control particles are blended with 5k control
particles sampled from the 3D model of the human figure
Results and Discussion
◇ The control flow with detailpreservation retains small-scale
fluid features
◇ The simulation was done using
LBM with a 240*120*120 grid
resolution which took 38s per
frame on average
◇ The computation of the control
forces took 2-4% of the total
computation time
Results and Discussion
◇ The mesh is only used to
generate a sequence of control
particles as described in Section 3.1
◇ We used 266k particles for the
SPH simulation which took 102s per
frame including the computation of
the control forces which took 14s
Results and Discussion
◇ Our detail-preserving approach clearly reduces
the artificial viscosity by the control forces
◇ The user can interactively adjust the parameters until the
desired coarse-scale behavior of the fluid is obtained
◇ Our framework could also be used to control the
deformation of elastic bodies
Conclusions
◇ A detail-preserving approach for controlling fluids based
on control particles
◇ We solve the problem of artificial viscosity introduced by
the control forces by applying these forces on the low-pass
filtered velocity field
◇ Only the coarse scale flow of the fluid is modified while
the natural small-scale detail is preserved, resulting in more
natural looking controlled simulations
References