Introduction to CFD Questions & Answers  


Hm, I don't understand the question. You need to explain better what you don't understand..






What does “alpha” mean? I didn't use this in class. You need to rephrase your question and use the same symbols as used in class. Or, define clearly a new symbol you are introducing.




Now I see what you mean. When dealing with a system of equations, the wave speeds are not necessarily $a$ or $u$. Rather, the wave speeds are the eigenvalues. So, when determining $F^\pm_{i+1/2}$, the wave speeds are within $\Lambda^\pm$ (those play the same role as the “$a$” does for a scalar equation). 1.5 point bonus.




Both $\phi=\max(0,\min(1,r))$ and $\phi=\max(0,\min(1,2r))$ respect the rule of the positive coefficients and reduce to first order at extrema and are hence valid. But $\phi=\max(0,\min(1,2r))$ is better because it is closer to the secondorder stencil. 1.0 point bonus.



$\pi$ 