Weakly nonlinear theories in electrohydrodynamics

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SUMMARY

The discussion centers on the challenges faced in modeling electrified fluid flow down a channel with a moving pressure distribution, specifically using a Benjamin-Ono like equation. The author has derived a numerical solution but encounters discrepancies when comparing it to an analytical solution obtained by neglecting the nonlinear term. The numerical results are off by a factor of ten, prompting inquiries about potential errors in the implementation or assumptions made during the analysis.

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  • Understanding of Benjamin-Ono equations
  • Proficiency in numerical methods for fluid dynamics
  • Familiarity with Fourier transforms
  • Knowledge of electrohydrodynamics principles
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  • Investigate numerical stability and convergence in fluid dynamics simulations
  • Explore error analysis techniques for numerical solutions
  • Learn about the implications of nonlinear terms in fluid equations
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Researchers and engineers in fluid dynamics, applied mathematicians, and anyone involved in electrohydrodynamics modeling who seeks to understand the complexities of numerical versus analytical solutions.

hunt_mat
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I have been working on the problem of electrified fluid flow down a channel with a moving pressure distribution. I have derived an equation which describes the free surface of said fluid flow which is a Benjamin-Ono like equation. I have a numerical solution for this equation and it gives the sort of pictures that I expect.

I can ignore the nonlinear part of the equation and I can an equation which I can solve analytically via Fourier transforms. Here is what is winding me up: When I set the nonlinear term to zero in my numerical code and compare it to my analytical solution, they should match but they don't, it's almost a factor of 10 out.

Has anyone come across this sort of thing happening before? Is it something I've done wrong?

Any suggestions are always welcome.

Mat
 

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