Detail-Preserving Fluid ControlDetail-Preserving Fluid Control

N. ThűreyR. KeiserM. Pauly

U. Rűde

SCA 2006

Abstract 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

IntroductionIntroduction

◇ Realism of fluids is important

[CMT04]

◇ The fluid controlling for animation is also important

[SY05b]

◇ Fine-scale detail such as small eddies or drops

IntroductionIntroduction

◇ 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

IntroductionIntroduction

◇ 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 WorkRelated 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 WorkRelated 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 WorkRelated 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 WorkRelated Work

◇ smoke[SY05a] and liquids[SY05b] matched the level set surface of the fluid with static or moving target shape

Fluid Simulation Models

Fluid Simulation Models

◇ We use two fluid simulation models to demonstrateour control method

◇ Smoothed Particle Hydrodynamics (SPH)

◇ The Lattice-Boltzmann Method (LBM)

Smoothed Particle Hydrodynamics (SPH)

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, ρ j : density of particle j

◇ Aj : the field quantity at rj

◇ W(r,h) : smoothing kernel with radius h

Smoothed Particle Hydrodynamics (SPH)

Smoothed Particle Hydrodynamics (SPH)

◇ Numerically solving the Navier-Stokes equations

The Lattice-Boltzmann Method (LBM)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)The Lattice-Boltzmann Method (LBM)

Streaming

◇ Streaming Collision Relaxation

The Lattice-Boltzmann Method (LBM)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 Fluid Control

◇ Generating Control Particles

◇ Controlling fluid using attraction force and velocity

force

◇ Detail-Preserving Control

Generating Control Particles 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 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 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

◇ Attraction force on a fluid element e

◇ : global contant that defines the strength of theattraction force

◇ if is negative, it will result in a repulsive force

Velocity 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 thevelocity force

Total 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

Detail-Preserving Control

◇ The velocity force lead to an averaging of the fluid velocities

◇ Undesirable artificial viscosity

◇ We want the natural small-scale fluid motion

Detail-Preserving Control Detail-Preserving Control

Detail-Preserving Control

Detail-Preserving Control

Detail-Preserving Control

Detail-Preserving Control

◇ Smoothed velocity field

◇ This smoothed version of the fluid velocity replacesV(e) in Equation 7

Detail-Preserving Control

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 DiscussionResults 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 DiscussionResults and Discussion

◇ The simulation using LBM with a 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

3300

Results and DiscussionResults and Discussion

◇ The control flow with detail-preservation 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 DiscussionResults 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 DiscussionResults 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

ConclusionsConclusions

◇ 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

ReferencesReferences