Help solving Simulink numerical oscillation

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SUMMARY

Tusike is addressing numerical oscillations in Simulink, specifically in systems with multiple chambers connected by valves. They have successfully calculated the amplitude of oscillation and established conditions for damping in a two-chamber system, with results aligning with Simulink simulations. However, Tusike is struggling to extend their mathematical formulation to higher-dimensional cases, having only achieved a solution for three chambers. They seek feedback on their mathematical approach and suggestions for expanding their findings to more complex systems.

PREREQUISITES
  • Understanding of Simulink for system simulations
  • Knowledge of oscillation theory and damping conditions
  • Mathematical formulation skills for multi-dimensional systems
  • Familiarity with fluid dynamics concepts related to chamber systems
NEXT STEPS
  • Research advanced Simulink modeling techniques for multi-chamber systems
  • Explore mathematical methods for analyzing oscillations in higher dimensions
  • Study fluid dynamics principles relevant to valve interactions in chamber systems
  • Investigate numerical methods for solving complex oscillation problems
USEFUL FOR

Engineers, researchers, and students working with Simulink simulations, particularly those focused on fluid dynamics and oscillatory systems in multi-chamber configurations.

Tusike
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Hi!

I posted a new thread about a week ago, but so far no one was able to help me:

https://www.physicsforums.com/showthread.php?t=761892

I wasn't sure if I posted in the right forum, so I'm posting it here hoping to reach a wider audience :)

Any help is greatly appreciated!

-Tusike
 
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Hi!

I think I found a solution to my problem in the case of two chambers connected by a valve.

I can calculate the amplitude of the oscillation that occurres, and have given a condition that leads to the oscillation damping, and my results agree with what I see in Simulink.
If anyone would go over my mathematical formulation given in the attachments, I would greatly appreciate that.

However, I'm having trouble expanding my math to more chambers = higher dimensional cases.
So far, I have been able to calculate the amplitude of oscillation for 3 chambers, but couldn't give a precise formulation of a solution such as in the 1D case. I will upload a document of my calculations for this as soon as I type it in.

I presented some ideas in the 1D case which could be used to expand to higher dimensions. If anyone could give me ideas on how to do that, and if the way I'm trying seems to be correct or not, I would also be very thankful.

Thanks!

-Tusike
 

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