Solving Partial Differential Equation Systems Numerically

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Discussion Overview

The discussion revolves around the numerical integration of a system of partial differential equations in cylindrical coordinates, specifically focusing on the continuity equation, momentum equation, and energy equation. The context includes challenges related to implementing the solution in Matlab or Fortran, with references to numerical methods such as the Crank-Nicholson method.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant seeks guidance on numerically solving a system of partial differential equations, mentioning the need for methods implemented in Matlab or Fortran.
  • Another participant questions whether the choice of Matlab or Fortran is due to familiarity, suggesting that Mathematica might be a more suitable tool for the task.
  • A participant expresses a strong preference for Matlab, citing extensive experience with the program and describing the problem as particularly challenging, related to "deflagration initiation by hot jets."
  • There is a request for websites that provide worked programs for computational fluid dynamics (CFD), indicating a desire for pre-existing solutions rather than developing a custom program.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the preferred software for solving the problem, with differing opinions on the suitability of Matlab, Fortran, and Mathematica. The discussion remains unresolved regarding the best approach to tackle the numerical integration.

Contextual Notes

Participants express varying levels of familiarity with the software options, which may influence their recommendations. The complexity of the problem is acknowledged but not fully explored in terms of specific numerical methods or implementation details.

Clausius2
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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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