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Courant number in 2D and 3D

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Old   October 26, 2009, 10:23
Default Courant number in 2D and 3D
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Wu Jian
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Hi.

Given the velocity as u, v and w separately for the x , y ,z direction.

How to define the Courant number in 2D and 3D?

Thank you so much.
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Old   October 26, 2009, 19:39
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You can use c0={sqrt[u^2+v^2+w^2]+c}dt/dx < 1 (assuming dx=dy=dz). If they are not equal you can try using dx=sqrt(dx1^2+dx2^2+dx3^2). For some schemes used for incompressible flows you might need c0 < 0.5.
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Old   October 27, 2009, 04:48
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Newton KF
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Hi folks... It is known that CFL criterium is linked to convective dominant problems. Is there another criterium when considering diffusive dominant or balanced diffusive-convective problems???

thanks...
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Old   October 27, 2009, 13:39
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For diffusion you can use \mu * dt / dx^2 =0.5.
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Old   October 27, 2009, 13:45
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Harishg, thanks for you reply... Can you indicate some papers that use this criterium???

thanks again...
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Old   October 27, 2009, 14:18
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The criterions are usually derived by using Von Neumann stability analysis. The use of the above criterion covers most of the methods. You can find detailed information on the stability criterion in the book of Hirsch.
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