Introduction to CFD Questions & Answers  
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?
04.29.17
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
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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.
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