Computational Aerodynamics Questions & Answers  
Question by Student 201327103
Professor, i check the boundary node and it looks like good. but the result still has same problem
This looks fine: your boundary conditions are well imposed. The contours you showed previously seem to have not been iterated at all. After the iteration process, are you reading in the data file (obtained after 1000 iterations or so) before outputting the post file?
Question by Student 201327132
Dear professor, I have a question about order of accuracy P. Assuming P>1, We obtained $GCI_f$. If P<1, Should we change to$\left\vert\frac{\triangle x_c}{\triangle x_f }-1\right\vert$? I obtained P that is smaller than 1 and minus value. Did I do it wrong way? Thank you.
Very good question. We made this assumption only when deriving the GCI. So, within the $\rm GCI_{f}$ equation, you should change the term to $\left\vert\left(\frac{\triangle x_c}{\triangle x_f }\right)^p-1\right\vert$. That is, the GCI should always be positive. However, when determining order of accuracy $p$, we did not use the GCI and we did not assume that $p$ should be greater than 1. So you should not change any of the equations used to determine $p$.
Question by Student 201427116
Professor, I have a question about WENO. We used below terms in WENO: $$ {\bar w_0} = \frac{\gamma_{0}}{{(\epsilon+\beta_0)}^2}, {\bar w_1} = \frac{\gamma_{1}}{{(\epsilon+\beta_1)}^2} $$ There is $\epsilon$ in denominator but what is it for? and how can I decide the value of $\epsilon$ ? $$ $$ Another question is about $\gamma_0$ and $\gamma_1$. With Taylor series expansion, we found $\gamma_0=\frac{1}{3}$ and $\gamma_1=\frac{2}{3}$ for 3rd order accuracy. With 3rd order accuracy, that is, WENO3, does $\gamma_0$ and $\gamma_1$ have fixed value of $\frac{1}{3}$ and $\frac{2}{3}$, respectively? Or are they also variants?
The user-defined constant $\epsilon$ is included to prevent a division by zero. Set it to a very small value. As for $\gamma_0$ and $\gamma_1$, they are fixed constants: don't change them.
Question by Student 201327132
Professor I have a question about bdry condition. In my note, One property must come from out of the domain at subsonic outflow bdry condition. So We choose Pressure. And We use $P_1^{n+1}=P_\inf$. Other bdry condition case that subsonic inflow, Two properties must be obtained from outside domain. So we choose Temperature and Pressure. And we use Stagnation Temperature and Pressure for time level n+1. Why we use difference methods to obtain pressure?(Stagnation pressure and Freestream pressure) Thank you.
For the inflow BC, the stagnation pressure can be assumed equal to the one in the freestream because the flow along a streamline is isentropic. But such is not the case for the outflow BC. What if there is a shock somewhere within the domain? Then, the entropy rises and the stagnation pressure will go down and not be equal to the one in the freestream. However, for external flows around a body, the pressure will eventually become equal to the freestream pressure even if shocks are present (as long as the BC is far away from the body). Hence why it's better at the outflow BC to choose to fix pressure rather than stagnation pressure.
Question by Student 201227138
Professor, I think I have bad luck bonus in your coruse, Viscous Flow. I will appreciate if you check my bad luck bonus.
OK, will look into this now.
Question by Prasanna
Professor, I am a bit confused about question #5 of Assignment 4. I have to find $$\frac{\partial F_3}{\partial U_4}=\frac{\partial (\rho u^2 +P)}{\partial U_4}=\frac{\partial (\rho u^2)}{\partial U_4}+\frac{\partial P}{\partial U_4}$$ and the difficult part seems to be in determining the $\frac{\partial P}{\partial U_4}$ term. The alternative method you taught involves using the chain rule, for example, $$\frac{\partial F_3}{\partial U_4}=\frac{\partial F_3}{\partial \rho_1} \frac{\partial \rho_1}{\partial U_4}+\frac{\partial F_3}{\partial \rho_2} \frac{\partial \rho_2}{\partial U_4}+\frac{\partial F_3}{\partial u} \frac{\partial u}{\partial U_4} +\frac{\partial F_3}{\partial \phi} \frac{\partial \phi}{\partial U_4} $$ where $F_3=F_3(\rho_1,\rho_2,u,\phi)$ and $\phi$ is some variable. For this problem, $\phi$ has to be a function of $U_1,U_2,U_3,U_4$ and also a function of P such that I can evaluate $\frac{\partial \phi}{\partial U_4}$. But then if I could express P in terms of $\phi$ which is a function of $U_1,U_2,U_3,U_4$, I would use the first method which you taught to evaluate the flux jacobian terms instead. I would like your comment regarding this.
You don't necessarily need to express $\phi$ as a function of $U$ to determine $\partial \phi/\partial U$ in the same way as you don't need to express $F$ as a function of $U$ to obtain $\partial F/\partial U$.
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