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#1 |
New Member
Join Date: Dec 2015
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Hello all,
I'm trying to get a better understanding of what the Courant number actually means. Therefore, I am trying to visualize it schematically. I know that, for example when using a first order upstream scheme, the information flows like this (see attachmant) when the Courant number is between 0 and 1. In this image, n = time and j = position. But how do these flows change when the Courant number changes? For example, I can't seem to figure out how to draw such a scheme with information flows when the Courant number is like -1, +2 or +3 or whatever. Can someone help me? (drawing these schemes would be very nice). Thanks in advance! |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,830
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Quote:
Do not consider negative values as they simply state the flow has negative direction (u<0). As you consider c>1, it simply states that c=u/(h/dt) = (dx/dt)/(h/dt) > 1. Geometrically, you have that the slope of the characteristic curve (dx/dt) is greater than the discrete counterpart (h/dt). In your sketch, the discrete curve has intersection with the axis tn outside (j-1,j). For example c= 2 intersects j-2, c=3 intersects j=3 and so on. In a first order upwind, you can intepret that fact as an extrapolation of the vlaues, which actually drives to a numerical instability. |
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#3 | |
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Quote:
Thanks for the quick reply. Does it then mean something like this? Thanks |
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#4 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,830
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yes, the green lines are the slopes of h/dt for increasing c number ...you see that they lie outside (j-1,j)
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