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
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
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
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?
 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.
 Question by Student 201127151 Professor, I have a question about the flux jacobian $A$. You explained that the scalar equation for a wave is $$\frac{\partial u}{\partial t} + a \frac{\partial u}{\partial x} =0$$ I understood that 'a' is a wave speed. And then you taught that the Euler equations for a wave in 1D is $$\frac{\partial U}{\partial t} + A \frac{\partial U}{\partial x} =0$$ Here, 'A' is the flux jacobian and I understood it mathematically. I think that it means the notion of a wave speed like 'a'. But I can't clearly comprehend the meaning of 'A'. What does it means exactly?
 04.11.17
Well the mathematical definition of $A$ is the flux jacobian, i.e. $$A\equiv \frac{\partial F}{\partial U}$$ This was mentioned in class. 0.5 point bonus.
 Question by Student 201127151 Professor, I am so curious about the boundary condition of the supersonic inflow. At question #1 - (a) of assignment #6, I find that the boundary condition is the supersonic inflow. So I think that all properties at node 1 are extrapolated externally as follows : $$T_1^{n+1}=T_{\infty},\; P_1^{n+1}=P_\infty,\; M_1^{n+1}=M_\infty$$ If so, I think $u_1^{n+1}$ and $v_1^{n+1}$ are also regarded as $u_\infty$ and $v_\infty$ respectively. Am I solving it correctly?
 04.28.17
Yes, that is correct. But you need to demonstrate why this is through the perpendicular Mach number and wave speeds. 2 points bonus.
Question by Student 201227141
Professor, inflow at BC when calculate update node1, we used $M^n_1$ to estimate subsonic or supersonic. But outflow at BC when calculate update node1, we used $M^n_2$ to estimate subsonic or supersonic. I am confused why these differences exist.
 05.01.17
Very good question. I made a mistake in class: always use $M_2^n$ to estimate whether the BC is subsonic of supersonic. Please change your notes accordingly. 2 points bonus boost.
 Question by Student 201427564 Professor, in assignment6, you asked to calcualte properties using 2nd degree polynomial. Can we calculate mach number using 2nd degree polynomial? Or 2nd degree polynomial just for temperature and pressure?
 05.03.17
You should use 2nd degree polynomials for all properties that are used to rebuild the $U$ vector at the boundary node (i.e., $u$, $v$, $T$, $P$). 1 point bonus boost.
 Question by Student 201227141 Professor, when subsonic inflow we used the equation like $T_0 = T(1 + 0.5(r-1)M^2)$. But we didn't use this at outflow. So I think this difference come from position of wing. I think there is no stagnation point at outflow. Am i right?
Hm no, there is always a stagnation point even if the flow does not come to a stop anywhere along the streamline. The stagnation point is imaginary. 1 point bonus.
 Question by Student 201227147 For subsonic outflow BC, you said that properties are extrapolated except $P_{1}^{n+1}$. And next, you wrote $u_{1}^{n+1}=2u_{2}^{n}-u_{3}^{n}$ and $v_{1}^{n+1}=2v_{2}^{n}-v_{3}^{n}$. At this case, can I just extrapolate them directly for subsonic outflow or should I follow the process that did for subsonic inflow?(obtaining $M_{1}^{n+1}$, $\alpha$, etc)
You can extrapolate them directly for subsonic outflow. There is no need to obtain the Mach number needed to obtain the pressure and temperature from the stagnation properties (which are not used for subsonic outflow). However, you first need to obtain the Mach number perpendicular to the boundary $M_\perp$ to determine the wave speeds and whether the boundary condition is subsonic outflow or supersonic outflow. 1 point bonus.
 05.04.17
 Question by Student 201427564 Professor, I have a question about deriving Grid coverage index (2nd May class). When you divide $$(\delta_{x} \phi)_{f} - (\partial_{x} \phi)_{f} = \frac {(\delta_{x} \phi)_{f} - (\delta_{x} \phi)_{c} } { 1 - ( \frac {\Delta x_{c}} {\Delta x_{f}} )^P }$$ by $$(\delta_{x} \phi)_{f}$$ you only divide numerator like this. $$1 - \frac { ( \partial_{x} \phi )_{f} } { (\delta_{x} \phi )_{f} } = \frac {(\delta_{x} \phi)_{f} - (\delta_{x} \phi)_{c} } {(\delta_{x} \phi)_{f}} \div( { 1 - ( \frac {\Delta x_{c}} {\Delta x_{f}} )^P } )$$ Why did you not divide denominator? I don't think this is just a mistake.
 05.07.17
Well, both the LHS and the RHS must be divided by the same amount. Thus, only the numerator on the RHS is altered. It wouldn't make sense to also divide the denominator.. 1 point bonus boost.
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