
[Sponsors] 
October 4, 2013, 06:09 
using time as a variable to classify a pde

#1 
New Member
nargess
Join Date: Oct 2013
Posts: 7
Rep Power: 5 
Hello Dear friends
I have a problem with classifying PDEs which is I don't know when to use 'time' as a variable for classifying the equations! I would be grateful if I can find the answer of my question as soon as possible. thanks alot 

October 4, 2013, 08:10 

#2 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,700
Rep Power: 33 
the time variable appears for parabolic, hyperbolic equations. Just consider a standard classification method for a PDE in terms of x1, x2, ...xn independent variables and assume x1=t.


October 4, 2013, 10:24 
is there anyone?

#3 
New Member
nargess
Join Date: Oct 2013
Posts: 7
Rep Power: 5 
Isn't there anyone who can help me about the socalled problem?


October 4, 2013, 10:43 

#4 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,700
Rep Power: 33 

October 4, 2013, 12:15 

#5 
New Member
nargess
Join Date: Oct 2013
Posts: 7
Rep Power: 5 
Thanks for your reply. I have studied Hoffman's CFD book, sometimes it uses only the coefficient matrix of d/dx to define the type of equation and somewhere else it uses the coefficient of time derivative either. for example in equation du/dt+a du/dx=0 , should i use time coefficient to determine the equation type?


October 4, 2013, 12:42 

#6  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,700
Rep Power: 33 
Quote:
Classification is done for PDE of the type: a(x1,...xn,f,..)*d2f/dx1^2 + ..... = 0 For example in a 2D case the PDE a* d2f/dx1^2 + b * d2f/dx1dx2 + c*d2f/dx2^2 =0 can be classified by analysing the characteristic curves. That can be found in many textbook. If am right, you can see the Hirsch book that uses the eigenvectors analysis 

October 4, 2013, 14:11 

#7 
New Member
nargess
Join Date: Oct 2013
Posts: 7
Rep Power: 5 
thank you so much, I will read the book.


October 6, 2013, 05:11 
another problem

#8 
New Member
nargess
Join Date: Oct 2013
Posts: 7
Rep Power: 5 
here is what I got :if 'time' derivative is of the highest order in a equation I have to use it's coefficients in chlassifying the equation or sytem of equation. am I right? for example in the following system
du/dt+a du/dx+b dv/dx=0 dv/dt+c du/dx+ d du/dx=0 but there is another question here: if we have a system like this:. du/dt+a du/dx+b dv/dy=0 dv/dt+c du/dx+ d du/dy=0 here we have 3 variables but as I studied in different books we just use d/dx and d/dy coefficient matrixes to classify the equation. 

October 6, 2013, 05:25 

#9  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,700
Rep Power: 33 
Quote:
You can use a matrix form of the system to write du/dt + A. du/dx+B. du/dy = 0 use u= uk*exp(i k.x) and develep an aigenvalue analysis 

October 6, 2013, 05:38 

#10 
New Member
nargess
Join Date: Oct 2013
Posts: 7
Rep Power: 5 
thank you so much.


Tags 
classifying, time 
Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to determine time step size and Max. iterations per time step.  pratik c  FLUENT  40  November 25, 2016 06:33 
pimpleFoam: turbulence>correct(); is not executed when using residualControl  hfs  OpenFOAM Running, Solving & CFD  3  October 29, 2013 09:35 
emag beta feature: charge density  charlotte  CFX  4  March 22, 2011 10:14 
IcoFoam parallel woes  msrinath80  OpenFOAM Running, Solving & CFD  9  July 22, 2007 02:58 
Replace periodic by inletoutlet pair  lego  CFX  3  November 5, 2002 21:09 