Computational Aerodynamics Questions & Answers  


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The problem with your logic is that $\partial \xi_x / \partial \xi$ is not zero because $\xi_x$ can vary along the the $\xi$ coordinate. Similarly, $\partial \eta_x / \partial \eta$ is also not zero because $\eta_x$ can vary along $\eta$. Good question, 2 points bonus.




The problem in your math is here: $$ \overset{\sim}{W_0}+\overset{\sim}{W_1}=\frac{1}{(\epsilon + \beta_0)^2+(\epsilon + \beta_1)^2} $$ This is not correct. Rather: \begin{align} \overset{\sim}{W_0}+\overset{\sim}{W_1}&=\frac{\gamma_0}{(\epsilon + \beta_0)^2}+\frac{\gamma_1}{(\epsilon + \beta_1)^2}\\ &=\frac{\gamma_0 (\epsilon + \beta_1)^2+ \gamma_1 (\epsilon + \beta_0)^2}{(\epsilon + \beta_0)^2(\epsilon + \beta_1)^2}\\ \end{align}




The cowl starts where the domain ends. So, there is no need to grid the cowl and there's hence no need to know the cowl length. The important thing is that your waves (either the Mach waves for the PrandtlMeyer compression fan case or the shock waves for the 3obliqueshock case) all meet at the same point and such a point is located exactly at the domain exit.



$\pi$ 