Solving the Orr-Sommerfeld equation with integral equation method in terms of the green function
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In this paper, an alternative method has been presented to solve the Orr-Sommerfeld equation in the linear theory of stability. To begin with, we define a Green function which is expressed in terms of matrix. Subsequently, its reciprocity has been shown. Finally, a linear integral equation equivalent to the original Orr-Sommerfeld equation is derived. The method is applied to the cases with two solid walls and any velocity distribution of the main flow at any Reynolds number.
KeywordsMathematical Modeling Reynolds Number Integral Equation Velocity Distribution Industrial Mathematic
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