Solving Partial Differential Equation Systems Numerically

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The discussion focuses on the numerical integration of a system of partial differential equations in cylindrical coordinates, specifically involving continuity, momentum, and energy equations. The Crank-Nicholson method is mentioned as a potential solution, with a request for guidance on implementing it in Matlab or Fortran. Users express preferences for Matlab due to familiarity, while one suggests Mathematica as a potentially easier alternative. The original poster seeks resources or websites with pre-implemented CFD programs to assist with their complex simulation task related to deflagration initiation by hot jets. The conversation highlights the challenges of numerical simulation and the desire for accessible solutions.
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I have to integrate numerically the next system of partial differential equations, in "r" and "z" coordinates (steady state, cylindrical coordinates):
-Continuity equation
-Momentum equation (with viscous and convection terms)
-Energy equation (with heat transfer, convection, and internal generation terms).
I heard something about Crank-Nicholson method. I have to implement this problem in Matlab or Fortran.
Anybody know about how can I solve this heavy task?
Anybody know about some web where I could obtain a method for solving it, and implemented in the software specified?.

Thanks for answering.
 
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Does it need to be in Matlab or Fortran, or are those the ones you know how to use?

It may be easier in Mathematica (my new favorite tool).
 
To be honest, Matlab is my useful program. I've been working with it very usually. I don't know anything about Mathematica.
This is the heaviest problem I've never simulated numerically.It is a part of a study of "deflagration initiation by hot jets".
 
I'm looking for a website holding worked programs of CFD. Do you know anyone?. I'm too lazy to do the program on my way!
 

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