Why Doesn't My Blasius Equation Script Match Fluid Mechanics Data?

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SUMMARY

The discussion centers on troubleshooting a Python script designed to solve the Blasius equation, which is yielding numerical results that do not align with established fluid mechanics data. Key issues identified include the need to verify input parameters and initial conditions, as well as experimenting with different values for the 'deta' and 'total' variables. The script utilizes libraries such as NumPy and Matplotlib for numerical calculations and plotting, respectively. Suggestions for improvement emphasize the importance of checking for errors and comparing results with reliable data sources.

PREREQUISITES
  • Proficiency in Python programming, particularly with libraries like NumPy and Matplotlib.
  • Understanding of the Blasius equation and its application in fluid mechanics.
  • Familiarity with numerical methods for solving differential equations.
  • Knowledge of data visualization techniques in Python.
NEXT STEPS
  • Investigate the impact of varying the 'deta' and 'total' parameters on the Blasius equation results.
  • Learn about numerical stability and convergence in solving differential equations.
  • Explore error-checking techniques in Python scripts to identify potential issues.
  • Review fluid mechanics literature to compare expected results with script outputs.
USEFUL FOR

This discussion is beneficial for fluid mechanics researchers, Python developers working on numerical simulations, and students seeking to understand the Blasius equation and its computational solutions.

javiergra24
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Hi everybody

I'm writing a script in Python to solve the Blasius equation but it does not work (well, script works and it generates the plot), numerical results does not match with data I've seen in fluid mechanics books.

Please anyone could help me? Thank you very much

Script is

Code: 
import sys, pylab, numpy
from pylab import *
from numpy import *
import matplotlib.pyplot as plt


deta=0.0001
total=10


e = []
f = []
g = []
h = []


fvec=0; gvec=0; hvec=0.3219

etavec=0.0

while etavec <= 10:

fvec = fvec + gvec * deta
gvec = gvec + hvec * deta
hvec = hvec -(1/2) * fvec * hvec * deta
etavec = etavec + deta
e.append(etavec)
f.append(fvec)
g.append(gvec)
h.append(hvec)
print etavec,fvec,gvec

numpy.savetxt("blasius.dat", transpose((e,f,g,h)),delimiter=' ')

pylab.figure()
pylab.plot(e,g)
pylab.plot(e,h)
xticklines = getp(gca(), 'xticklines')
yticklines = getp(gca(), 'yticklines')
xgridlines = getp(gca(), 'xgridlines')
ygridlines = getp(gca(), 'ygridlines')
xticklabels = getp(gca(), 'xticklabels')
yticklabels = getp(gca(), 'yticklabels')
#lines1 = pylab.plot(e,f)
lines2 = pylab.plot(e,g)
lines3 = pylab.plot(e,h)
#pylab.setp(lines1, color='b', linewidth=3.0)
pylab.setp(lines2, color='r', linewidth=3.0)
pylab.setp(lines3, color='k', linewidth=3.0)
setp(xticklines, 'linewidth', 3)
setp(yticklines, 'linewidth', 3)
setp(xgridlines, 'linestyle', '--')
setp(ygridlines, 'linestyle', '--')
setp(yticklabels, fontsize='xx-large')
setp(xticklabels, fontsize='xx-large')
xlabel('$\eta$',fontsize=30)
ylabel('$f(\eta) \quad \partial_{\eta} f(\eta) \quad \partial_{\eta \eta}f(\eta)$',fontsize=30)
axis([0.0,10,-0.9,20.9])
#legend( (lines1, lines2, lines3), ('$\f(\eta)$', '$\partial_{\eta} f(\eta)$', '$\partial_{\eta \eta}f(\eta)$'))


grid(True)
pylab.show()
 
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Hi there,

Thank you for sharing your script and the issue you are facing. It can be quite frustrating when the results don't match with the expected data. I would be happy to help you troubleshoot the issue and suggest some possible solutions.

Firstly, have you checked the input parameters and initial conditions in your script? It's important to make sure they are correct and match with the data you are comparing with.

Secondly, have you tried using different values for deta and total? Sometimes, changing these parameters can make a difference in the results.

Also, it would be helpful to see the data you are comparing with and the specific differences you are observing. This can give us a better idea of where the issue might be.

Lastly, have you tried checking for any errors or warnings in your script? Sometimes, these can point towards the source of the discrepancy.

I hope these suggestions help and I am looking forward to hearing back from you with more information. Good luck with your script!