[chusma]

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.

Thank you for your attention

[FMDenaro]

What's wrong with your solution?

[chusma]

Originally Posted by FMDenaro

What's wrong with your solution?

Thanks for your answer

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.

[FMDenaro]

Divergence can be due to a numerical stability issue... check for the step value, does it satisfy the constraint?

[chusma]

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.

[FMDenaro]

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.

[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.

[chusma]

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