| Topic: |
Science > Physics |
| User: |
"A. Boom" |
| Date: |
01 Apr 2005 11:48:01 PM |
| Object: |
Simple fluid dynamics model |
Hi,
I am a physics student.
I desire to numerically simulate the dynamics of a two-dimensional gas
subjected to a constant gravitational field and driven on the upper
boundary by a given function. Energy of the system can be dissipated by
the remaining three boundaries or assuming some simple radiation loss
function. I'm not too concerned with how the system dissipates the
energy, only that it do so in some reasonable manner. The model need
only give a pressure field or velocity field; something to measure wind
direction and magnitude by.
The idea is to have an initial density for the gas and then input energy
to the system on the upper boundary, which can simulate the radiation
from the Sun. If the intensity is greatest at the midpoint of the upper
boundary, I think that two circular wind currents will result. I hope
that the equations used will result in some chaotic behavior. It would
be wonderful to see, but I don't know much of anything about chaotic
systems.
I've never performed a numerical simulation. I'm wanting to combine what
I'm learning in a numerical processing course and atmospheric physics
course. This model seems to be enough to model simple winds. The model
is not intended to be precise, but to show the qualitative behaviour of
wind generation. For instance, the midpoint of the horizontal axis could
represent latitudes near the equator and the resulting wind patterns
like those near the tropics.
I've not learned any fluid mechanics; just classical, quantum, and am
learning general relativity. The problem appears to be a fluid dynamics
one, which I'm trying to approximate as best I can using classical
mechanics.
An equation which I derived is
Del(P(x,y,z,t)) = -rho(x,y,z,t)[a(x,y,z,t) + g*k_hat], where P is the
pressure, rho the density, a the acceleration, g the gravitational
acceleration, and k_hat the unit vector in the +z direction. It was
arrived at by using F=ma for a cube of constant mass subjected to
pressure and gravitational fields.
I derived it in three dimensions because I wished to involve density.
For the model I can simply assume that there is not change in the y
direction. The model will be in x and z.
What I implicitly assumed when deriving the equation is that the mass of
the cube, as it moves, is constant. I now believe that this may not work
for my model because the density will change at a point (x,y,z) in time.
All the mathematical models that I derive rely ultimately on the density
function. For the initial density condition I can use the hydrostatic
equilibrium equation. However I do not know how to model a change in
density with an increase in energy at a specific (x,y,z), as would
happen at the upper boundary.
A few questions.
In the model of a two-dimensional gas, if thermal energy is given to an
infinitely small volume centered at a point (x,z), how can the change in
density of that point and surrounding points be calculated? It seems
that energy given to an isolated region will, in time, be distributed
among the entire system. What methods can be used to figure this out? It
seems to be at the heart of the model.
I'd appreciate readers' help in this matter, Adam.
.
|
|
| User: "Rene Tschaggelar" |
|
| Title: Re: Simple fluid dynamics model |
02 Apr 2005 02:07:42 PM |
|
|
A. Boom wrote:
Hi,
I am a physics student.
I desire to numerically simulate the dynamics of a two-dimensional gas
subjected to a constant gravitational field and driven on the upper
boundary by a given function. Energy of the system can be dissipated by
the remaining three boundaries or assuming some simple radiation loss
function. I'm not too concerned with how the system dissipates the
energy, only that it do so in some reasonable manner. The model need
only give a pressure field or velocity field; something to measure wind
direction and magnitude by.
The idea is to have an initial density for the gas and then input energy
to the system on the upper boundary, which can simulate the radiation
from the Sun. If the intensity is greatest at the midpoint of the upper
boundary, I think that two circular wind currents will result. I hope
that the equations used will result in some chaotic behavior. It would
be wonderful to see, but I don't know much of anything about chaotic
systems.
I've never performed a numerical simulation. I'm wanting to combine what
I'm learning in a numerical processing course and atmospheric physics
course. This model seems to be enough to model simple winds. The model
is not intended to be precise, but to show the qualitative behaviour of
wind generation. For instance, the midpoint of the horizontal axis could
represent latitudes near the equator and the resulting wind patterns
like those near the tropics.
I've not learned any fluid mechanics; just classical, quantum, and am
learning general relativity. The problem appears to be a fluid dynamics
one, which I'm trying to approximate as best I can using classical
mechanics.
The subject involves the fluid dynamic, thermo dynamic, finite element
computations, 3D modelling, specifying grids according to estimates and
and enormous amouts of computing time. Using the currently standard
tools it takes you several months to get familiar with them.
Classical mechanics is sufficient for fluid dynamic modelling.
However since this subject is vast when applied to normal
problems, I suggest you first finish your study while picking up a
semester on fluid dynamic modelling and have a look at it after the
diploma. Then the required PC floating point power again increased.
Rene
--
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net
.
|
|
|
| User: "A. Boom" |
|
| Title: Re: Simple fluid dynamics model |
02 Apr 2005 07:20:13 PM |
|
|
Rene Tschaggelar wrote:
The subject involves the fluid dynamic, thermo dynamic, finite element
computations, 3D modelling, specifying grids according to estimates and
and enormous amouts of computing time. Using the currently standard
tools it takes you several months to get familiar with them.
Classical mechanics is sufficient for fluid dynamic modelling.
However since this subject is vast when applied to normal
problems, I suggest you first finish your study while picking up a
semester on fluid dynamic modelling and have a look at it after the
diploma. Then the required PC floating point power again increased.
Rene
Hi Rene,
I'm appreciative of your response. What I'm after is not an accurate
model of the atmosphere, but just a model that is simple enough to
exhibit wind circulation-like behaviour. I've been reading about finite
difference methods, which I now know how to apply to a system of
differential equations. The problem at this point is which system of
equations will result in wind-like behaviour. I've read about
Navier-Stokes equations, atmospheric primitive equations, but all are
overly complex for what I want to. Deriving the equation I presented
earlier is the closer to what I'd like to model. However, it has the
problem of not working with varying density.
I've looked into two-dimensional fluid dynamics models, however they do
not seem to model wind circulation, rather they model fluid streams as
they pass around objects. Like for aerodynamics. I do not know what the
name or subject for what I'm trying to model is. Fluid dynamics seemed
the obvious choice.
I realize it is not simple, but surely there is a simple enough model
that I can numerically simulate.
Do you know of any basic ideas that I would need to use to apply in a
derivation? Can I play known equations for a global gas to an
infinitesimal volume of gas and thereby turn them into local relations?
Thanks, Adam.
.
|
|
|
| User: "Rene Tschaggelar" |
|
| Title: Re: Simple fluid dynamics model |
04 Apr 2005 06:13:35 AM |
|
|
A. Boom wrote:
Rene Tschaggelar wrote:
The subject involves the fluid dynamic, thermo dynamic, finite element
computations, 3D modelling, specifying grids according to estimates and
and enormous amouts of computing time. Using the currently standard
tools it takes you several months to get familiar with them.
Classical mechanics is sufficient for fluid dynamic modelling.
However since this subject is vast when applied to normal
problems, I suggest you first finish your study while picking up a
semester on fluid dynamic modelling and have a look at it after the
diploma. Then the required PC floating point power again increased.
I'm appreciative of your response. What I'm after is not an accurate
model of the atmosphere, but just a model that is simple enough to
exhibit wind circulation-like behaviour. I've been reading about finite
difference methods, which I now know how to apply to a system of
differential equations. The problem at this point is which system of
equations will result in wind-like behaviour. I've read about
Navier-Stokes equations, atmospheric primitive equations, but all are
overly complex for what I want to. Deriving the equation I presented
earlier is the closer to what I'd like to model. However, it has the
problem of not working with varying density.
I've looked into two-dimensional fluid dynamics models, however they do
not seem to model wind circulation, rather they model fluid streams as
they pass around objects. Like for aerodynamics. I do not know what the
name or subject for what I'm trying to model is. Fluid dynamics seemed
the obvious choice.
I realize it is not simple, but surely there is a simple enough model
that I can numerically simulate.
Do you know of any basic ideas that I would need to use to apply in a
derivation? Can I play known equations for a global gas to an
infinitesimal volume of gas and thereby turn them into local relations?
Athmosphere physics is not my main subject, so I have to
keep it short. The gaz equations, namely adiabatic
compression is used to explain certain phenomena such as
warm winds coming from down the mountains when there is
precipitation on the other side.
The gaz equations are equlibrium equations and are thus
ill suited to describe the athmosphere in one go.
You have a pressure profile built from gravity, distorted
by temperature gradients. Then the flowing athmosphere
has some mass density distribution in vertical direction,
that makes a thin flows compared to the distance the air flows.
Note that every 5500m, the air pressure halfes, making it
practically vanish above 15000m, that is where the troposphere
ends. Compare this to the distance of a low to a high pressure
zone, usually 1000's of km separated.
As soon as you have multiple phases such as gaz and fluid
or gaz and solid, solar radiation changes for the ground below,
surface effects for evaporation and condensation of the droplets
or ice cristals come into play. The energy storage in this
precipitation has some delay compared to the gaz equations and
the drops/cristals move in the gavitational field. Not necessarily
down.
Whatever subset of theories you apply, you'll encounter
situations when the model breaks down and gives false results.
I'm still waiting for a model of a thunder cloud to produce
a halfway realistic movie.
Rene
.
|
|
|
|
|
|
|
Related Articles |
|
|
