Prandtl-Meyer Function Iteration

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SUMMARY

The discussion centers on implementing the Prandtl-Meyer function iteration in MATLAB to calculate the value of nu for a given Mach number (M). The equation provided is nu = sqrt((gamma +1)/(gamma -1))*atan(sqrt((gamma - 1)/(gamma +1)*(M^2-1)))-atan(sqrt(M^2-1)). Users are encouraged to explore numerical methods such as the Newton-Raphson method for this purpose, as there are no built-in MATLAB functions available for this specific calculation without additional toolboxes.

PREREQUISITES
  • Understanding of the Prandtl-Meyer function and its mathematical formulation
  • Familiarity with MATLAB programming and syntax
  • Knowledge of numerical methods, specifically the Newton-Raphson method
  • Basic understanding of fluid dynamics concepts, particularly Mach number
NEXT STEPS
  • Research how to implement the Newton-Raphson method in MATLAB
  • Explore MATLAB's optimization toolbox for potential functions that could assist in root-finding
  • Study the Prandtl-Meyer function in detail to understand its applications in compressible flow
  • Look into alternative numerical methods for solving equations, such as the bisection method or secant method
USEFUL FOR

Engineers, physicists, and MATLAB programmers involved in fluid dynamics and compressible flow analysis who need to calculate the Prandtl-Meyer function for various Mach numbers.

nanvinnie
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hi.. I'm trying to write a MATLAB code that will iterate the mach value given a certain value for nu.

nu = sqrt((gamma +1)/(gamma -1))*atan(sqrt((gamma - 1)/(gamma +1)*(M^2-1)))-atan(sqrt(M^2-1))

this is the equation for the prandtl-meyer function, but how do i write it in MATLAB so that i can extract the value of nu for a given M value? sort of like the goal seak function in excel...

i would appreciate anyone's help!
 
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I don't know of any built-in MATLAB function that does this for you (without any additional toolboxes, that is), but that doesn't mean there isn't one...

I would look into something like the Newton-Raphson's method (but there are many others). The wikipedia article on Newton's Method is pretty good, and at the bottom is a list of similar algorithms. It's not difficult to write some algorithm like this for MATLAB.

-Kerry
 

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