Introduction to CFD Questions & Answers  
Question by Student 201227147
Professor, in the section 2 of the table (Euler Equation in Generalized Coordinates), it says that $Q \equiv \Omega U$. But I guess it should be $Q \equiv \Omega \Gamma U$.
True, but $\Gamma=1$, so it doesnt' matter in this case. 1 point bonus.
Question by Student 201327132
Professor, This is answer of thursday question. It is not relate that mesh doesn't change in time.
This is great! 2.0 points bonus. I would have given you 3 points bonus if you would have typeset it using .
Question by Student 201327132
Professor, Assignment 2 deadline is described Tuesday 29th March. So That confused me.
Its due on Thursday. I fixed the mistake.
Question by Student 201327133
Professor, I have a question about τ. I understood that η and ξ mean each line number of horizontal and vertical grid. But i don't know what is physical meaning of τ. If i know that, it much easier to understand the class.
$\tau$ is the same as $t$ because we set $\Gamma$ to 1. 1 point bonus.
Question by Student 201327103
Professor, I think the problem is $i$ and $x$ are not in same direction. In previous example, $i$ axis and $x$ axis are in same direction. So that computer can decide $x$ component first with setted space and than decide $y$ component form equation $$ y=sin(15x/L)H/20 $$ Here the space doesn't change with $y$ But in this problem space change with $x$ and $y$. So, computer may not find proper point of nodes which have setted space through $x^2+y^2=r^2$. Because I don't know the computer codes in detail, I can't approach to the solution.
You're on the right track. It has something to do with the fact that it's difficult to find a root for $y$ on a circle at $x=\pm r_{\rm i}$. Because the method used to solve the equation within the Equation() command is a Newton-Raphson non-linear root solver, it may fail close to $x=\pm r_{\rm i}$ depending on the initial guess or the size of the first $\Delta x$ given to the solver. Say for example that $x$ is at $-r_{\rm i}$ and $\Delta x$ is set to $-10^{-10}$ m, then this will result in a negative value for $y^2$ in the Newton-Raphson procedure, and the Equation command will fail. I'll explain this better through an example next class. 2 points bonus.
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