Computational Aerodynamics Questions & Answers


B. Parent • AE68714 Computational Aerodynamics

Computational Aerodynamics Questions & Answers

Question by Student 201238707

when we found velocity vector $u^{n+1}_1$ $\&$ $v^{n+1}_1$. we extrapolated $u^{n+\frac {1} {2}}_1$ $\&$ $v^{n+\frac {1} {2}}_1$. And we put $\theta^{n+\frac {1} {2}}_1 = \theta^{n+1}_1$ then used $$\theta^{n+1}_1 = atan(\frac{v^{n+1}_1}{u^{n+1}_1})= atan(\frac{\alpha*v^{n+\frac{1}{2}}_1}{\alpha*v^{n+\frac{1}{2}}_1})$$ but i wonder why those $\theta$ are same?

06.05.17

I don't understand. What other value would you give it?

Question by Student 201227147

Professor, in the section 2 of the table (Euler Equation in Generalized Coordinates), it says that $Q \equiv \Omega U$. But I guess it should be $Q \equiv \Omega \Gamma U$.

06.06.17

True, but $\Gamma=1$, so it doesnt' matter in this case. 1 point bonus.

Question by Student 201327132

Professor, This is answer of thursday question. It is not relate that mesh doesn't change in time.

03.19.18

This is great! 2.0 points bonus. I would have given you 3 points bonus if you would have typeset it using LATEX.

Question by Student 201327132

Professor, Assignment 2 deadline is described Tuesday 29th March. So That confused me.

03.24.18

Its due on Thursday. I fixed the mistake.

Question by Student 201327133

Professor, I have a question about τ. I understood that η and ξ mean each line number of horizontal and vertical grid. But i don't know what is physical meaning of τ. If i know that, it much easier to understand the class.

$\tau$ is the same as $t$ because we set $\Gamma$ to 1. 1 point bonus.

Question by Student 201327103

Professor, I think the problem is $i$ and $x$ are not in same direction. In previous example, $i$ axis and $x$ axis are in same direction. So that computer can decide $x$ component first with setted space and than decide $y$ component form equation $$ y=sin(15x/L)H/20 $$ Here the space doesn't change with $y$ But in this problem space change with $x$ and $y$. So, computer may not find proper point of nodes which have setted space through $x^2+y^2=r^2$. Because I don't know the computer codes in detail, I can't approach to the solution.

03.27.18

You're on the right track. It has something to do with the fact that it's difficult to find a root for $y$ on a circle at $x=\pm r_{\rm i}$. Because the method used to solve the equation within the Equation() command is a Newton-Raphson non-linear root solver, it may fail close to $x=\pm r_{\rm i}$ depending on the initial guess or the size of the first $\Delta x$ given to the solver. Say for example that $x$ is at $-r_{\rm i}$ and $\Delta x$ is set to $-10^{-10}$ m, then this will result in a negative value for $y^2$ in the Newton-Raphson procedure, and the Equation command will fail. I'll explain this better through an example next class. 2 points bonus.

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