Viscous Flow Questions & Answers  
Question by Student 201427102
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Wow! thank you! professor! I got some result!! However there still is another error message... Is it okay???
If this error appears, it means the way you impose the coefficients violates the memory space. I.e., you are reading or writing outside of the bounds for *a, *b, *c or *rhs. Check your coefficients again, there is a bug there somewhere..
Question by Student 201527110
Professor, today we derived $\overline{\Phi}_{x'=-L_t}$ using Taylor series but, you took partial derivate of $\overline{\Phi}$ with $x$. In my opinion, we have to take derivative of $\overline{\Phi}$ with $x'$ because we had considered $\overline{\Phi}$ over $X'-Y'$ coordinate. Is it okay to take partial derviative with x then x'?
You are absolutely right. It would have been more clear to take the partial derivative with respect to $x^\prime$. But the partial derivative with respect to $x$ is not affected by a change in reference frame, so this wouldn't change the end result.
Question by Student 201327107
Professor, I have a question about assignment8 question3. How can I find $\tau_w $ without information about the initial conditions?
The *mut contains $\mu_{\rm t}$ from the previous iteration (or from the initial condition if at the first iteration). Of course, for this to work, you need to update the coefficients and *mut within the function find_coeff_and_rhs().
Question by Student 201427102
Professor,I have questions about turbulent viscosity.
1. When find wall shear stress, we need $\mu_{t,j=1.5}$, and it was $$\mu_{t,j=1.5} = \frac { \mu_{t,j=1} + \mu_{t,j=2}}{2}$$ but $\mu_{t} = {\rm something\;long\;term}\; y^{2}$,then how can be $\mu_{t,j+\frac{1}{2}} = \frac { \mu_{t,j+1} + \mu_{t,j}}{2}$
2. how discretize $|\frac{∂u}{∂y}|_j$?
It doesn't matter if $\mu_t$ is a long expression or not. Find it at the nodes first, and then calculate at the interfaces by taking the average of the nearby nodes. A simple approximation to $\partial u / \partial y$ is $(u_{j+1}-u_{j-1})/(2\Delta y)$. We'll see this tomorrow.
Question by Student 201327103
Professor, this is my code for turbulent flow. I can have symmetric shape answer for this code, but ub is five times bigger than answer. And I don't know what is wrong.
turbulent flow.txt    
Did you check if your answer is grid-converged? I.e., if changing $N$ by 2 times does not result in a major change in $u_b$?
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