How Can I Solve the Orr-Sommerfeld Equation Using Finite Difference Methods?

[URIA]

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Hy
I trying to solve the orr sommerfeld diff equation using numerical methods. the best candidate in my point of view is a finite difference. can someone help with this?
Much appreciated
Uria

Hy
I trying to solve the orr sommerfeld diff equation (plane Couette flow case) using numerical methods. the best candidate in my point of view is a finite difference. can someone help with this?
Much appreciated
Uria

 

[_coyote_]

Ra'ananYou can try using a finite difference method to solve the Orr–Sommerfeld equation. You can start by discretizing the equation with the central difference scheme and then use an iterative approach such as the Gauss–Seidel method to solve the resulting system of equations. This approach has been used in the past to solve this type of equation numerically. You can find more information about this in the following references:1. F. Hussain, “Numerical Solutions of the Orr-Sommerfeld Equation for Plane Couette Flow,” Journal of Computational Physics, vol. 14, no. 1, pp. 65–76, 1974.2. J. P. Verboncoeur, “A Numerical Method for the Solution of the Orr-Sommerfeld Equation in Plane Couette Flow,” AIAA Journal, vol. 31, no. 3, pp. 513–515, 1993.3. M. R. Visbal, “Numerical Solution of the Orr-Sommerfeld Equation in Plane Couette Flow Using Finite Difference Method,” International Journal of Numerical Methods in Fluids, vol. 23, no. 8, pp. 783–796, 1997.