Computational Aerodynamics Questions & Answers  
Question by Student 201127151
Professor, I have a question about $\Omega$. You said that ${\Omega}={x_{\xi}}{y_{\eta}} + y_{\xi}x_{\eta}$ and it means the area of a cell. I understood that $\Omega$ represents area because its dimension is $[m^2]$. But I don't understand that it is the area of a cell. Is it just the definition, or can we demonstrate it?
03.17.17
Good question. I have pondered this as well when I first encountered the generalized coordinates.. The definition of $\Omega$ is simply ${x_{\xi}}{y_{\eta}} + y_{\xi}x_{\eta}$, not the cell area. But it is very close to the cell area thus. In the next assignment, I will ask you to compare the cell area with $\Omega$ and assess the differences. I'll give you 2 points bonus.
Question by Student 201427142
Professor, I still cannot understand about $\Gamma$ in quastion by student #201527110 $$ \Phi_1 = U \frac{\partial}{\partial\tau}\left(\Omega\Gamma\right) = U \frac{\partial}{\partial\tau}\left(\frac{\partial x}{\partial\xi}\frac{\partial y}{\partial\eta}\frac{\partial\tau}{\partial t}-\frac{\partial y}{\partial\xi}\frac{\partial x}{\partial\eta}\frac{\partial\tau}{\partial t} \right) $$ at here $$\frac{\partial}{\partial\tau}\left(\frac{\partial x}{\partial\xi}\frac{\partial y}{\partial\eta}\frac{\partial\tau}{\partial t}\right) = \left(\frac{\partial}{\partial\tau}\left(\frac{\partial x}{\partial\xi}\right)\right)\frac{\partial y}{\partial\eta}\frac{\partial\tau}{\partial t}+\frac{\partial x}{\partial\xi}\left(\frac{\partial}{\partial\tau}\left(\frac{\partial y}{\partial\eta}\right)\right)\frac{\partial\tau}{\partial t}+\frac{\partial x}{\partial\xi}\frac{\partial y}{\partial\eta}\left(\frac{\partial}{\partial\tau}\left(\frac{\partial\tau}{\partial t}\right)\right)$$ and I understand 1st and 2nd in right term. But I think that the 3rd term($\left(\frac{\partial}{\partial\tau}\left(\frac{\partial\tau}{\partial t}\right)\right)$) cannot be omitted. Because $\frac{\partial\tau}{\partial t}$ is still depending on $\tau$. How can we assume $\Gamma = 1$??
We can set $\Gamma$ to any value as long as it respects the dependency we originally specified. That is, $\Gamma=\partial\tau/\partial t$ should be such that $\tau=\tau(t)$. Thus, we can choose $\Gamma$ to be $1$ or $t$ or $t^2$ but not $x$ or $tx$, etc. Here, it is perfectly fine to choose $\Gamma=1$. One advantage of choosing $\Gamma=1$ is that $$ \frac{\partial}{\partial\tau}\left(\frac{\partial\tau}{\partial t}\right) = \frac{\partial}{\partial\tau}\left(\Gamma\right) = \frac{\partial}{\partial\tau}\left(1\right) = 0 $$ If $\Gamma$ would have been chosen as $t$ or $t^2$, then the latter wouldn't be 0, and this would lead to $\Phi_1\ne 0$, and this would prevent us to write the Euler equations in generalized coordinates in conservative form. I'll give you 2 points bonus boost.
Question by Student 201427564
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Professor, When I try to open warp file through 'Pluma', this error occured. How should I do?
03.26.17
Warp is a binary file (executable), so it can not be opened in pluma. With pluma you can open text files like .wrp or .txt or .c etc. Please don't do assignment #4 now: the tgz package is not complete yet. I'll explain what to do in assignment 4 tomorrow.
Question by Student 201427564
Professor, I wonder about difference between 'EE' and 'NO'. 'E' makes mesh equally space and 'NO' also. Can we adjust distance with 'E' like below? Block(is,js,ie,je, EE,0.5,2,2, NO); Also, is it right that 'NO' only makes mesh equally 1? (like default) I know this is very basic question but I want to know clearly. Thank you.
03.27.17
Hmm, I am not sure what your first question is.. As for the second, 'NO' does not make the mesh equally 1, it simply needs to be used when the block is 1D (when there are no segments along a certain dimension). I'll give you 1 point bonus boost.
Question by Student 201427102
1.jpg  ./download/file.php?id=3370&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3370&t=1&sid=a869392a3cf326d111f6d3db39292f6a
for middle block, you use "BLOCK(    ,GG,   );"
2.jpg  ./download/file.php?id=3368&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3368&t=1&sid=a869392a3cf326d111f6d3db39292f6a
for middle block, you use "JOINT(    ,GG,   );"
3.jpg  ./download/file.php?id=3369&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3369&t=1&sid=a869392a3cf326d111f6d3db39292f6a
However, this case, for middle block, you use "JOINT(   ,EE,   );" Why I shoud use 'EE' rather than 'GG'??
First, the command is Join(), not Joint(), and is case sensitive. So, if you use JOIN or join it will not work: it has to be spelled Join. For the third mesh, you can not use Join(is,js,ie,je,j,GG..) because the GG segment grabs the spacing from the mesh along the j coordinate. So in this case, he will set the first grid spacing (between j=js and j=js+1) to the distance between the point (i,js-1) and the point (i,js). However, there is no point (i,js-1) because it is outside of the domain. Good question: 2 points bonus boost.
Question by Student 201227147
Professor, I have a question about the today's class. During the class, to set $js1$ which is the midpoint of $js$ and $je$, you wrote as follow: $$js1 = round(0.5*(je-js));$$ but if I set $js = 40$ and $je = 100$, $js1$ becomes 30 which is not located between $js$ and $je$. Similarly, you wrote $is_1$ as follow: $$is1 = round(((ie-is)-0.7*(ie-is))/2);$$ but if I set $is = 40$ and $ie = 100$, $is1$ becomes 9 which is also not located between $is$ and $ie$. Could you tell me what I'm thinking wrong?
03.28.17
You are not wrong.. Rather, I forgot to include some term. It should have been written: $$ \rm js1=round(0.5 * (je-js))+js; $$ and $$ \rm is1=round(0.3*(ie-is)/2)+is; $$ Good observation: 2 points bonus boost.
Question by Student 201227106
Professor, I think Assignment 3 has a problem. In question #2, Q is consist of omega*U, but I think Q is consist of omega*capital gama*U.
03.29.17
That's right: I fixed it. I'll give you 1 point bonus boost because your typesetting was hard to read.
Question by Student 201227141
Professor, Q3 in Assignment3 is finding $G_η$ at nodes. Althogh Eqation has Ω, it did not need to calculate. Then is it not problem whatever Ω's value is?
03.30.17
Yes, absolutely, you don't need to calculate $\Omega$ in this case. But if you choose not to calculate it, you have to explain clearly how $\Omega$ cancels out. Once $\Omega$ disappears from the terms, then there is of course no need to calculate it. Good observation: 2 points bonus.
Question by Student 201427102
naninani.PNG  ./download/file.php?id=3378&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3378&t=1&sid=a869392a3cf326d111f6d3db39292f6a
after write "paraview post.grid", that message appear. How can I solve this problem?
“ERROR: In /build/paraview-arsa8T/paraview-5.0.1+dfsg1/ParaViewCore/ServerImplementation/Core/vtkSIProxy.cxx, line 310 vtkSISourceProxy (0x3b3f430): Failed to create vtkXdmfReader. Aborting for debugging purposes. Aborted (core dumped)”
03.31.17
Well, the file name should end with .vtk in order to be read in paraview.. I'll give you 1 point bonus boost.
Question by Student 201427564
.png  ./download/file.php?id=3383&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3383&t=1&sid=a869392a3cf326d111f6d3db39292f6a
Professor, I have a question about last Tuesday class. In attached figure, You coded is=1, js=1 in line 8. But you put zero in command 'Corners' in line 27. It works well but I can not understand. Please explain the reason. Also, I think is3 should be declared before is2. Because is2 contains is3. Am I right?
04.01.17
The first two zeros in the Corners() command are for the $x$ and $y$ positions of the lower-left corner. The next two values are for the $x$ and $y$ positions of the upper-right corner. For the second question, yes, if is2 depends on is3, then you should initialize is3 before initializing is2. Two points bonus boost.
Question by Student 201427564
.PNG  ./download/file.php?id=3384&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3384&t=1&sid=a869392a3cf326d111f6d3db39292f6a
Professor, when you did this example you coded Block1 and Block4 again(I mean you coded twice for one block.). When I try to coded only {Block1 again!} and {Block4 again!}, it did not work. Could you explain me the reason?
04.03.17
Hm, I don't understand what could be wrong.. You need to explain this more carefully.
Question by Student 201227141
Professor, I think i did assignment. And i found export button in paraview but i could't see the bottom side of the export page. So i just pushed enter of my keyboard but exporting didn't work. How can i do well?
1234.png  ./download/file.php?id=3386&sid=a869392a3cf326d111f6d3db39292f6a  ./download/file.php?id=3386&t=1&sid=a869392a3cf326d111f6d3db39292f6a
1234_.png
04.04.17
An easy way around this is by moving the window so you can see the buttons at the bottom. You can move the window by pressing the key “alt”, the left mouse button, and moving the mouse around. Alternately, you can increase the resolution of your screen, but this is more involved..
Question by Student 201527110
Professor, in my opinion, we have to consider about the change of properties when flow pass through the shock for the supersonic flow example you explained today, but there was any no mention about shocks. Could you explain why we can ignore the changing of properties by shock?
04.06.17
Hmm, I didn't mention about the shock today and there is no reason to at this stage.. But I'll give you 0.5 point bonus for the effort.
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