* imagis is a joint project of cnrs, inria, inpg and ujf. phenomenological simulation of brooks...
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* iMAGIS is a joint project of CNRS, INRIA, INPG and UJF.
Phenomenological Simulation Phenomenological Simulation
of Brooksof Brooks
Phenomenological Simulation Phenomenological Simulation
of Brooksof Brooks
Fabrice Neyret Nathalie Praizelin
iMAGIS / GRAVIR - IMAG *
http://www-imagis.imag.fr/
iMAGIS-GRAVIR / IMAG
If CFD had to be usedIf CFD had to be usedIf CFD had to be usedIf CFD had to be used Very thin resolution, large domainVery thin resolution, large domain
( and stability very small dt ) Very non-linear equations Very non-linear equations (shockwaves, surf. tension) Hard and long system solvingHard and long system solving Unknown parameters Unknown parameters (e.g. boundary conditions) Visible features are emerging phenomenaVisible features are emerging phenomena
Hard to control Hard to control
whilewhile Water motion is not directly visibleWater motion is not directly visible Strong a priori knowledge on the resultStrong a priori knowledge on the result Users want some controlUsers want some control
[FM96,97,...](Navier-Stokes)
iMAGIS-GRAVIR / IMAG
If surface wave simulation had to be usedIf surface wave simulation had to be usedIf surface wave simulation had to be usedIf surface wave simulation had to be used
Very thin resolution, large domainVery thin resolution, large domain Very non-linear equations Very non-linear equations (waves trigger waves) Hard and long system solvingHard and long system solving
whilewhile Strong a priori knowledge on the resultStrong a priori knowledge on the result
[FR86,P86,GS97]
iMAGIS-GRAVIR / IMAG
If Fourier synthesis had to be usedIf Fourier synthesis had to be usedIf Fourier synthesis had to be usedIf Fourier synthesis had to be used
Very thin resolution, large domainVery thin resolution, large domain Non-linear phenomenaNon-linear phenomena Non uniform wave propagationNon uniform wave propagation
(variable depth, obstacles) Statistical models are helplessStatistical models are helpless
whilewhile Strong a priori knowledge on the resultStrong a priori knowledge on the result Users want some controlUsers want some control
[MWM87,TDG00,Areté]
iMAGIS-GRAVIR / IMAG
Relying on phenomenological simulationRelying on phenomenological simulationRelying on phenomenological simulationRelying on phenomenological simulation
Primitives based:Primitives based:
Geometric construction of visual featuresGeometric construction of visual features
Choice of the primitives of visual interestChoice of the primitives of visual interest User can control the primitivesUser can control the primitives ““Vector primitives”: Vector primitives”:
independent from rendering resolution independent from rendering resolution Fast, high resolution, large domainFast, high resolution, large domain
iMAGIS-GRAVIR / IMAG
cg
cw
gravity waves:
capillary waves: cg = 3cw 2
cg = 1cw 2
shallow water: cg = cw (cst)
h = 8 cmh = 4 cm
h = 2 cmh = 1 cmh = 0.5 cm
h = 0.25 cm
h = 8 cm
h = 4 cm
h = 2 cm
h = 1 cm
h = 0.5 cm
k
cw
gravity wavescapillary waves
shallow water
Wave theoryWave theoryWave theoryWave theory
iMAGIS-GRAVIR / IMAG
Wave theoryWave theoryWave theoryWave theory
ω2 = gk+γρk3⎛
⎝ ⎜ ⎞
⎠ ⎟ tanhkh( )
k=2πλ
ω=2πT
=2πf
QuickTime™ et un décompresseurGIF sont requis pour visualiser
cette image.
QuickTime™ et un décompresseurGIF sont requis pour visualiser
cette image.
QuickTime™ et un décompresseurGIF sont requis pour visualiser
cette image.
cg =∂ω∂k
cg
cw
gravity waves:
capillary waves: cg = 3cw 2
cg = 1cw 2
shallow water: cg = cw (cst)
h = 8 cmh = 4 cm
h = 2 cmh = 1 cmh = 0.5 cm
h = 0.25 cm
cw =λT
=ωk
capillary waves: cg > cw
gravity waves: cg < cw
shallow water: cg = cw
iMAGIS-GRAVIR / IMAG
vc
c= gh
vc
c= gh
vc
c= gh
Typology of stationary wavesTypology of stationary wavesTypology of stationary wavesTypology of stationary waves
non dispersive case:cg = cw = c
shockwave
vc
capillary waves triggered by a shockwave
ccgg
capillary waves
ccww
ccgg
gravity waves (dispersives) ccww
ccgg
iMAGIS-GRAVIR / IMAG
Froude waves - shockwaves calculationFroude waves - shockwaves calculationFroude waves - shockwaves calculationFroude waves - shockwaves calculation
vc
vc
vc
c= gh
Fr = Fr = VV cc
sin(sin() =) = 1 1 FrFr
(Froude number)
(slope)
iMAGIS-GRAVIR / IMAG
Froude waves - shockwaves calculationFroude waves - shockwaves calculationFroude waves - shockwaves calculationFroude waves - shockwaves calculation
vc
c= gh
Fr = Fr = VV cc
sin(sin() =) = 1 1 FrFr supercritical (Fr > 1)
subcritical (Fr < 1)
fast (Fr > 2)
iMAGIS-GRAVIR / IMAG
The chosen primitivesThe chosen primitivesThe chosen primitivesThe chosen primitives
iMAGIS-GRAVIR / IMAG
Our approachOur approachOur approachOur approach
1. Get a stationary velocity field (low res is ok)
2. Build the primitives skeletons
3. Add field perturbations [WH91]
4. ( Build a surface and render )
iMAGIS-GRAVIR / IMAG
1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field
iMAGIS-GRAVIR / IMAG
1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field
iMAGIS-GRAVIR / IMAG
1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field
iMAGIS-GRAVIR / IMAG
1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field
iMAGIS-GRAVIR / IMAG
supercriticalsupercritical (Fr > 1) (Fr > 1)
subcriticalsubcritical (Fr < 1) (Fr < 1)
iMAGIS-GRAVIR / IMAG
2. Build the primitives skeletons2. Build the primitives skeletons2. Build the primitives skeletons2. Build the primitives skeletons
1.2
2.4
0.3
1.5
1.8
0.8
1.6
0.4
1.31.2
1.8 0.9
1.1
0
iMAGIS-GRAVIR / IMAG
2. Build the primitives skeletons2. Build the primitives skeletons2. Build the primitives skeletons2. Build the primitives skeletons
iMAGIS-GRAVIR / IMAG
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.QuickTime™ et un décompresseur
sont requis pour visualisercette image.
3. Add field perturbations3. Add field perturbations3. Add field perturbations3. Add field perturbations
[WH91]
Small support fields (vortex,source)
attached on particles (passive floaters)
iMAGIS-GRAVIR / IMAG
A perturbation needs time to propagate:
We cannot simply apply the static construction !
A node moves if: V changes locally the previous node has moved
perturb V >>
perturb V >>
3. Add field perturbations3. Add field perturbations3. Add field perturbations3. Add field perturbations
iMAGIS-GRAVIR / IMAG
3. Add field perturbations3. Add field perturbations3. Add field perturbations3. Add field perturbations
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
QuickTime™ et un décompresseur sont requis pour visualiser
cette image.
iMAGIS-GRAVIR / IMAG
Conclusion - limitations - future workConclusion - limitations - future workConclusion - limitations - future workConclusion - limitations - future work A real-time simulation of (some)
animated visual features of brooks ! Vectorial construction (no grid sampling)
Perturbations can be random, procedural (von Karman),or user generated.
Fade and stop the primitives. Adaptive capillary ripples. Define a rendering method !
(producing a surface ?) Hydraulic jumps, foam, ...
* iMAGIS is a joint project of CNRS, INRIA, INPG and UJF.
Phenomenological Simulation Phenomenological Simulation
of Brooksof Brooks
Phenomenological Simulation Phenomenological Simulation
of Brooksof Brooks
Fabrice Neyret Nathalie Praizelin
iMAGIS / GRAVIR - IMAG *
http://www-imagis.imag.fr/
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