# Boundary Value Problem for CFD Case

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July 11, 2017, 08:23
Boundary Value Problem for CFD Case
#1
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Chus Mat
Join Date: Feb 2017
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I am currently very frustrated with this problem. Is a Boundary Value Problem for ODEs system as an approach of quasi-steady one dimensional flow in a rocket combustion chamber. The equations have the shape on the picture eq.

The ideal gass state equation closes the system.

The BC's are: At the beginning of the domain as Initial Values: T(0) = value; u(0) = 0, aprox. And at the end of the domain as clossure, the mass flow provides the condition shown in the picture b.c

Must be assumed the values which are not the flow magnitudes (ρ,p,T,u)are known.

I am currently applying a finite differences approach with an Explicit Euler's for the ODEs. I have a lot of problems to choose the best method for this problem. I have tryed with different ideas, the most recent was the Shooting Method with the secant method for the nonliniarrity.

I am very lost with this problem and it is the main part of my Bachelors Degree Thesis, so I would appreciate any help.

Attached Images
 Eq.PNG (10.9 KB, 13 views) bc.PNG (4.0 KB, 5 views)

 July 11, 2017, 10:34 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,255 Rep Power: 67 What's wrong with your solution?

July 11, 2017, 10:38
#3
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Chus Mat
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Quote:
 Originally Posted by FMDenaro What's wrong with your solution?

The problem is that my scheme diverges during the iteration of the shooting method.

I have not so much experience in this kind of programming and I do not know how to avoid or prevent that situation.

If there is another scheme or method that could be more suitable, please tell me.

 July 11, 2017, 10:42 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,255 Rep Power: 67 Divergence can be due to a numerical stability issue... check for the step value, does it satisfy the constraint?

July 11, 2017, 14:11
#5
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Chus Mat
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Quote:
 Originally Posted by FMDenaro Divergence can be due to a numerical stability issue... check for the step value, does it satisfy the constraint?
Which constraint are you talking about?

Excuse my ignorance.

July 11, 2017, 14:32
#6
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Filippo Maria Denaro
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Quote:
 Originally Posted by chusma Which constraint are you talking about? Excuse my ignorance.
If you are not familiar with numerical methods for solving ODE, I strongly suggest reading this subject on a good textbook of numerical analysis.
Numerical stability is one of the major issue in explicit methods and you definitely need to take care of that.

 July 11, 2017, 14:34 #7 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,255 Rep Power: 67 Note that you are working with a system of first order ODE, so be carefull in you boundary conditions to ensure that the mathematical problem is well posed.

July 11, 2017, 14:38
#8
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Chus Mat
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Quote:
 Originally Posted by FMDenaro Note that you are working with a system of first order ODE, so be carefull in you boundary conditions to ensure that the mathematical problem is well posed.
The problem comes from the shooting method iteration, not from the explicit scheme, however.

The scheme is made to converge but the iteration is not. I would like to fix that