* imagis is a joint project of cnrs, inria, inpg and ujf. phenomenological simulation of brooks...

* iMAGIS is a joint project of CNRS, INRIA, INPG and UJF.

Phenomenological Simulation Phenomenological Simulation

of Brooksof Brooks


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)


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]


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]


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


Phenomena that are out of scope


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


Wave theoryWave theoryWave theoryWave theory

ω2 = gk+γρk3⎛

⎝ ⎜ ⎞

⎠ ⎟ tanhkh( )

k=2πλ

ω=2πT

=2πf

QuickTime™ et un décompresseurGIF sont requis pour visualiser

cette image.


cette image.


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


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


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)


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)


The chosen primitivesThe chosen primitivesThe chosen primitivesThe chosen primitives


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 )


1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field1. Get a stationary velocity field


supercriticalsupercritical (Fr > 1) (Fr > 1)

subcriticalsubcritical (Fr < 1) (Fr < 1)


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


2. Build the primitives skeletons2. Build the primitives skeletons2. Build the primitives skeletons2. Build the primitives skeletons


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)


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 >>





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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.


of Brooksof Brooks


of Brooksof Brooks

Fabrice Neyret Nathalie Praizelin

iMAGIS / GRAVIR - IMAG *

http://www-imagis.imag.fr/


Le détail des mouvements est complexe :


Exploite-t-on toute la connaissance disponible ?Exploite-t-on toute la connaissance disponible ?Exploite-t-on toute la connaissance disponible ?Exploite-t-on toute la connaissance disponible ?

Il y a de grandes régularités dans les scènes naturelles !

* imagis is a joint project of cnrs, inria, inpg and ujf. phenomenological simulation of brooks...

Documents

c w slide

c g c w gravity waves

c g c w shallow water

v c sin

imagisgravir imag slide

large domain slide

gs97 slide

aret slide