Kam, Hyeong Ryeol

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3 Νοε 2013 (πριν από 3 χρόνια και 1 μήνα)

56 εμφανίσεις

http://kucg.korea.ac.kr

http://kucg.korea.ac.kr

Kam, Hyeong Ryeol

http://kucg.korea.ac.kr


Abstract


Introduction


Related Work


Simulation of Cumuliform Cloud Formation


Our Control Method for Cloud Formation


Controlling Cloud Simulation


Results


Discussion and Future Work


Conclusion


Appendix

http://kucg.korea.ac.kr


Cloud play an important role for creating realistic
images


The atmospheric fluid dynamics already exists


But difficult to adjust parameters and the initial status


So, we focus on


Controlling cumuliform cloud formation


The user specifies the shape of the clouds


Automatically adjusts parameters to form that shape

http://kucg.korea.ac.kr


Although CFD(Computational fluid dynamics)
methods can generate realistic shapes and motion, it is
difficult for the user to control the simulation result
and impossible to adjust the parameters manually.


In previous methods, the motion of smoke and water
such as letters and animals has been calculated.


In this paper, we focus on controlling cloud formation.


http://kucg.korea.ac.kr


We only focus on cumuliform clouds(
적운
).


Our method generates realistic clouds.


The user specifies the contours of the clouds.


Previous approach did not produce convincing results
because there are several physical processes

: phase transition from water vapor to water droplets




We developed a new method that controls the
physical parameters affecting the cloud formation
process.

http://kucg.korea.ac.kr


Fluid Control


After the pioneering work by Treuille et al. [2003]


Control smoke and water by using the adjoint method


McNamara et al [2004]


Control smoke by adding external forces


Fattal and Lischinski [2004]


Calculate the motion of smoke by using a potential field


Hong and Kim [2004]


Feedback control mechanism


Shi and Yu [2005], Kim et al [2007]


SIMILAR, but NOT directly APPLICABLE to CLOUDS


Since physical phenomena involved in cloud formation is not
concerned.

http://kucg.korea.ac.kr


Fluid Control


More recently,


Control the motion of water by using control particles


Thurey et al. [2006]


Make smoke move along a user
-
specified path


Kim et al. [2006]


There are NO methods for controlling the formation of
clouds based on computational fluid dynamics

http://kucg.korea.ac.kr


Cloud Simulation


1. procedural techniques


Generate the density distribution of clouds using the idea of
fractals.


Ebert et al [2002]


Modeling without generating 3d density distributions


Trembilski and Brobler [2002], Bouthors and Neyret [2002],
Neyret [1997], Gardner [1985]



Although the cost is very low and it’s possible to generate the
desired cloud shapes, a trial and error process is required.

http://kucg.korea.ac.kr


Cloud Simulation


2. physical simulation of formation process


Generate clouds by numerical simulation


Dobashi et al [2000], Kajiya and Herzen [1984], Miyazaki et al
[2001], Miyazaki et al [2002], Harris et al [2003]



Although these methods have the potential to generate
realistic clouds, many physical parameters have to be
adjusted to generate convincing results.


Adjusting the parameters MANUALLY is almost impossible.

http://kucg.korea.ac.kr


The numerical simulation of cumuliform cloud
formation












(b) the temperature of the rising air currents decreases due to
adiabatic cooling.


(c) the latent heat is liberated, which creates additional
buoyancy forces and promotes further growth of the clouds.


Our method mainly controls the amount of latent heat.



http://kucg.korea.ac.kr


The density of air is assumed to be constant


The atmosphere is assumed to be an incompressible
and inviscid fluid media.



http://kucg.korea.ac.kr


The motion of the atmosphere is expressed by Navier
-
Stokes equations



,



B : buoyancy force / f : an external forces (such as wind)







T : the temperature / z=(0,0,1)


/ k
b

: the buoyancy coefficient


T
amb

: the ambient temperature, inverse
-
proportion to the height


1
st

term : proportional to the difference between the
temperature of the rising air parcel and the surrounding air


2
nd

term : the drag force due to the falling water droplets




http://kucg.korea.ac.kr


The phase transition between the water vapor and the
clouds



,





,


C
c

: the amount of clouds generated by the phase transition


S
v

: the amount of water vapor /
α
: the phase transition ratio


q
s

: the saturation vapor content


If C
c

< 0 then, the amount of clouds q
c

is reduced


It means : the evaporation of water droplets




http://kucg.korea.ac.kr


The temperature






Γ
d

: the adiabatic lapse rate


ω

: the
z

component of the fluid velocity


Q : the coefficient of the latent heat


S
T

: the heat supplied from the ground


1
st

term : the advection by the flow field



2
nd

term : the adiabatic cooling of rising air



3
rd

term : the latent heat


The amount of the latent heat is assumed to be proportional to
the amount of cloud generated by the phase transition



http://kucg.korea.ac.kr


T
0
(the initial temperature)=T
amb
(the ambient temp)


q
v,0
(the initial water vapor)


Decrease exponentially from the bottom of sim. space


The initial temperature and water vapor


Are constant in the horizontal direction


q
c,0
(the initial cloud density) = zero


u
0
(the initial velocity) = zero


For the boundary conditions,


A periodic boundary condition is used in the horizontal


A fixed boundary condition(
u
=0) is used on the bottom
and top of the simulation space

http://kucg.korea.ac.kr



pink curve = the desired shape



The contour line is projected onto
a plane perpendicular to the xy
component of the vector
connecting the viewpoint and the
center of the simulation space



3d shape(target shape) is
generated from the contour line

http://kucg.korea.ac.kr


Our method controls the simulation


so that the difference between the target shape and the
simulated clouds becomes zero


The effect of wind is not concerned


Since it doesn’t contribute very much to the ccf


The convection due to the buoyancy force is the main
driving force for the cumuliform clouds.



http://kucg.korea.ac.kr


To measure the difference, we use the height ratio R of
the top of the simulated clouds to the top of the target
shape.








http://kucg.korea.ac.kr


Key features in our control method


1. Feedback control


adjusts the vertical extent of the clouds



2. Geometric potential field


adjusts the horizontal extent of the clouds


http://kucg.korea.ac.kr


1. Feedback controller


Promotes the cloud growth until the clouds reach the
top of the target shape (
R
(
i
,
j
)=1.0)


2. Geometric potential field


When the target shape is not a height field, the clouds
may grow outside of the target shape


So, geometric potential field is used


External forces preventing the clouds from growing outside


We use only the horizontal components of the external
forces.

http://kucg.korea.ac.kr


1. Feedback controller


Cloud growth is promoted by controlling the latent heat
and by supplying additional water vapor


2 functions


The latent heat controller


controls the coefficient for the latent heat Q (old :
constant
).


-

updates Q
c
(i,j) that was for the grid point (i,j,0) as a control variable


-

the coefficient for latent heat for grid point (i,j,k) = Q
c
(i,j)


The water vapor supplier


adds water vapor where clouds does not reach the top of the target shape
(old:
at the bottom of the simulation space

+ top

of the clouds)


-

determines the amount of water vapor, S
v,c
(i,j), to be supplied


There are N
x
*N
y
*2 control variables


To adjust these parameters, we employ PID controller


PID=proportional
-
integral
-
derivative

http://kucg.korea.ac.kr


2. Geometric potential field


is generated in a preprocessing step so that the potential
value becomes large inside the target shape


The external forces are generated in proportion to the
gradient of the potential field.


As a result, the external forces prevent clouds from
growing outside the target shape.



http://kucg.korea.ac.kr


How our control mechanism works?


1. Compute the height ratio R(i,j)


Ratio is sent to latent heat controller, the water vapor supplier


2. the water vapor supplier


determines the amount of the water vapor, S
v,c


and adds this at the grid points corresponding to the top of
the simulated clouds.


Promotes the phase transition from water vapor to clouds.



http://kucg.korea.ac.kr


How our control mechanism works?


3. the latent heat controller


Increases Q
c

where the clouds have not reached the top of
the target shape (R(i,j)<1.0)


Q
c

increases the temperature when the clouds are generated
due to the phase transition


The increase in temperature results in an increase in the
buoyancy force


This promotes the cloud growth to higher regions.


4. During cloud growth


The external forces due to the geometric potential field push
clouds inwards the inside the target shape



http://kucg.korea.ac.kr


How our control mechanism works?


5. As the clouds approach the top of the target shape


The water vapor supplier decreases the amount of additional
water vapor .


The latent heat controller also stops increasing the latent
heat coefficient


6. So, user
-
specified clouds are generated automatically



The simulation is terminated manually by the user


After done, the details might be reduced because the control
forces could prevent vortices and detail from developing



http://kucg.korea.ac.kr


1. The generation of the target shape


2. The geometric potential field


3. The feedback control of the simulation


4. The water vapor supplier



http://kucg.korea.ac.kr


The target shape is generated from the user specified
contours of the desired cloud shape.


1. the user specifies the generating region


The center of the simulation space is placed at the center of
the specified region


2. the user draws the contours on the screen


3. the contours are projected onto a plane


4. the target shape is generated


Thickens the 2d sketch by extracting its medial axis


5. a bounding box of the target shape is generated and is
subdivided into a 3d grid


Grid is used to compute the geometric potential field and to
simulate the cloud formation process

http://kucg.korea.ac.kr


1. An initial potential field is generated


1 : inside grid points


0 : outside grid points


2. Applying a 3d Gaussian filter to the initial field in
order to create a smooth and continuous potential
field


The result field is the geometric potential field.

http://kucg.korea.ac.kr


During simulation,


F, the external force due to the geometric potential filed
is calculated at each grid point


Because of using only the horizontal component of F,








q
c

: the density of clouds /
ψ

: the potential field


Since the external force is proportional to the gradient of the
potential field, it only works near the boundary of the target
shape.


No external forces are generated at the grid points where no
clouds exist since F is also proportional to q
c

http://kucg.korea.ac.kr


updates the coefficient for the latent heat, Q
c
(i,j)


Using PID control mechanism
-
> PI control







∆H(i,j) : the normalized height difference between the top of the clouds
and the target shape


http://kucg.korea.ac.kr





1
st

term : proportional controller


K
P

: proportional gain


When only using this, small gaps between the simulated
clouds and the target shape are left (So, 2
nd

term is needed)


Not counting when clouds grow near the top of the target shape,


Because ∆H becomes very small



2
nd

term : integral controller


Contributes when the accumulated difference becomes large


D : Duration for the accumulation / K
I

: integral gain


Removes the gaps and updates Q
c

until ∆H becomes zero


http://kucg.korea.ac.kr


The control parameters need to be specified.


We determine K
P

and K
I

experimentally


It is difficult to determine all these parameter


From experiments, we found that larger values are required
for K
P

and K
I

where the top of the target shape is high


Because the cloud growth in such regions has to be promoted
further than the regions where the top of the target shape is low.


We assume that K
P

and K
I

are proportional to the height
of the target shape.





к
P
,
к
I

: proportionality coefficients


Ĥ
target

: the height of the target shape divided by the height of the
simulation space.


As a result, к
P
,
к
I
are specified by the user.

http://kucg.korea.ac.kr


Adds water vapor


if



Indicates that the water vapor is supplied at the grid points
where the ratio R(i,j) < the average of the ratios


The water vapor supplier tries to make the ratio of the cloud
growth the same for all grid points




The top of the cloud at all grid point reaches the top of the
target shape almost simultaneously.


The amount of additional water vapor





C
v

: a control parameter for the water vapor supplier, specified by
the user / q
v,0
: the initial water vapor at the beginning


(i,j,k
top
) : the grid point corresponding to the top of the clouds


http://kucg.korea.ac.kr


Intel Core2 Extreme X9650 with nVidia GeForce 8800
GTX


The simulation space : 320 * 80 * 100 grid


The average computation time for each time step of
the simulation : 7 seconds


The additional computational cost due to control
mechanism is very low and is less than one percent of
the total computation cost

http://kucg.korea.ac.kr


к
P
=4.95,
к
I
=0.6, c
v
=0.5


c
v

is from process of trial and error


Once the appropriate values for these parameters have
been found, we can generate various shapes of clouds


http://kucg.korea.ac.kr


Comparing to Fattal’s method






In Fattal’s method, clouds are generated where they
should not be


Our method can generate realistic clouds while their
shapes closely match the target shapes.


http://kucg.korea.ac.kr


Case that is not the height field

http://kucg.korea.ac.kr


The target shapes are completely different from height
fields.

http://kucg.korea.ac.kr


Generating clouds resembling real clouds in a photo

http://kucg.korea.ac.kr


Our control mechanism is fairly indirect.


Feedback controllers cannot guarantee that the clouds
will completely form the desired shape.


The indirect control makes it possible to promote the
cloud growth as naturally as possible (realistic
-
looking)


The indirect control allows the user to specify the rough
shape of the clouds and finally generate the realistic
clouds.

http://kucg.korea.ac.kr


Our method controls the cloud motion in the vertical
direction


The horizontal movement of the clouds is not controlled


Since the forces due to cloud formation work only in the
vertical direction


It is difficult to control the horizontal movement by
controlling the cloud formation process


The previous fluid control methods might be suitable
for horizontal control




it is expected that the combination of methods to control
the cloud motion in both vertical and horizontal directions.


http://kucg.korea.ac.kr


Our method can handle a desired shape that is not a
height field.


However, it is still difficult to handle a shape that is very
different from a height field




the cumuliform cloud formation process affects the
vertical movement of the clouds


Horizontal external forces are required


Our goal for generating realistic clouds forming the
desired shape has been achieved.


Extending the method to handling multiple target
shapes is our next important research direction

http://kucg.korea.ac.kr


The user specifies the shape of clouds viewed from
only a single direction.




solution : to specify the multiple target shapes viewed
from multiple viewpoints.


Ziegler
-
Nichols method doesn’t always provide ‘good’
parameters.


A trial and error process is still required.


Extension of our method to other types of clouds such
as stratus is also an interesting area for future work


http://kucg.korea.ac.kr


Controlling cumuliform cloud simulation


Our method can generate clouds with desired shapes


Controlled by our feedback controller and external
forces calculated by the geometric potential field.


For feedback control, we developed a latent heat
controller and a water vapor supplier.


By controlling the amounts of latent heat and
additional water vapor, clouds grow naturally and
converge into the desired shape


Our method provides a simple way to generate realistic
clouds with desire shapes

http://kucg.korea.ac.kr


We determine к
P
,
к
I

based on this method


1. Experimental simulations are carried out several
times with the proportional controller only.


2. Carried out with increasing
к
C

and the controller tries
to make the clouds reach a target height


In experiment, the target height is set to 80% of space


When
к
C

is small, the clouds cannot reach


As
к
C
increases, the clouds can reach


At a certain value of
к
C
, the cloud growth exhibits periodical
oscillations




Clouds repeatedly exceed and fall below the target height


2. T
C

: the period of the oscillation







http://kucg.korea.ac.kr


Any questions?