Computational Aerodynamics Questions & Answers  
Question by Student 201327133
Professor, i have a question about ximax. You showed us that ximax being similar as zero when state is steady. I run the code about Question #3, and i've got the result about time,iter,etc... but there is no more less than 1.0E+3 at ximax. but i can't believe that it could be zero... is it correct result? or are there more exact solution?
As I explained today, ximax probably won't go down to zero for your problems if you use the TVD Van Leer limiter or WENO. The residual will thus “hang”. So, you can't rely on ximax to determine convergence. You need to proceed differently as explained in class.
Question by Student 201227111
Professor, I don't understand what the value from -opm command mean exactly. At first, I thought it was the average of values at x=x_station and y=(node1 to node 60). So, I extract data at i=2,10,20,30,40,50,60 and j=1 to 60 using "-pr" command. And averaging each value, And compare to value obtained from "-opm command" with varying x_station. (compare density, Temperature, velocity) When i is small, "-opm" value is similar to my average value. But the bigger the i, the bigger the difference. When i=60, "-opm command" value is similar to average value of i=60, j=1 to 20(only 1/3 nodes). So, I'm stuck here, I don't what to do after. Sorry about my poor explanation.
I need more information. Please show a plot of the pressure contours. Also, show your code in the Post() module. Further, how are you invoking warp with -opm? I hope you read in your data file... Otherwise, this will simply post-process the initial conditions..
Question by Student 201227111
Professor! I bring more explain about previous question. I wanted to know the meaning of Post() modules command to compute mass flux average stagnation pressure.
plot.png  ./download/file.php?id=4214&sid=3dba1a5b80ea71b08bf8c7cd2df16708  ./download/file.php?id=4214&t=1&sid=3dba1a5b80ea71b08bf8c7cd2df16708
I simply gridding like this.(ie=60, je=60, dx is constant) Result is like this.
And My post code is same as original, only changing x_station[1] set to L-1e-5 (L is length of inlet)) and for loop range set 1 to 1.
And I use "warp -r design3.wrp -i data.1500 -op post60.1 -pt gnuplot -pr 60 1 60 60" this command, I get properties that x is fixed in one line and y is vary.(like above picture) And, use matlab code, I compute average of each properties($\rho$, $T$, $q$). Then, I compare this average value to value that obtained from "warp -r design3.wrp -i data.1500 -opm". (Because properties vary along y axis but using "warp -r design3.wrp -i data.1500 -opm" is give only one value)
then my computed average value is $\rho=0.2774$, $T=467.5837$, $q=2403.5$, but value obtained by "-opm command" is $\rho=0.6730$, $T=789.1027$, $q=2297.65$.
I think value obtained by Post() module is average of value on fixed x line, but it isn't. It only work when i is very small(only 2 or 3..). So I want to understand about meaning of value that obtained by Post() module. or I think something wrong?
Everything seems fine except your matlab values. Are you doing a simple averaging using matlab? This will of course be wrong. You need to do a mass flux averaging (do $\frac{1}{\dot{m}}\int P d\dot{m}$ in matlab not $\frac{1}{H}\int P dy$).
Question by Student 201327103
professor this is my counter plot for cylinder.
I can't get shock wave. I Think my boundary condition is wrong, but i don't know where is wrong. here is my code
The problem may be that you are imposing free stream boundary conditions on all boundary nodes..? You should check your boundary conditions are well imposed using the -on flag.
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 $\partial F/\partial U$.
Question by Van Tien
Professor, in Assignment 5, Question #3, for the extrapolation, I am confused to use the 1D-Lagrange interpolation or 2D-Lagrange interpolation. In the case of 1D-Lagrange interpolation, I am not sure the polynomial function is based on x or y coordinate. In the case of 2D-Lagrange interpolation, I think I need more information from the other nodes.
Use a 1D extrapolation polynomial. 2D is too time consuming to compute.
Question by Student 201983196
Professor, in Assignment7, Question#2, How do I calculate this equation, $\frac {\mid{A}\mid (Z_L,Z_R)}{2}(U(Z_R)-U(Z_L))$? Is $\frac {\mid{A}\mid (Z_L,Z_R)}{2}$ 2X1 matrix? But $(U(Z_R)-U(Z_L))$ also is 2X1 matrix? I don't know how to calculate $F_(i+\frac{1}{2})=\frac{F(Z_L)+F(Z_R)}{2}+\frac {\mid{A}\mid (Z_L,Z_R)}{2}(U(Z_R)-U(Z_L))$
No, $|A|$ is a $2 \times 2$ matrix determined from an average state function of $Z_L$ and $Z_R$.
Question by Prasanna
Professor, for Assignment #7, Question #3, are the answers posted in the following order: $u_L$,$u_R$ in decimal digits, $u_R$ in fraction, $f(u_L)$ in decimal digits, $f(u_L)$ in fraction respectively?
I updated the answers to make them more clear.
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