# Courant number in 2D and 3D

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 October 26, 2009, 10:23 Courant number in 2D and 3D #1 Member   Wu Jian Join Date: Jun 2009 Location: Poitiers Posts: 33 Rep Power: 10 Sponsored Links 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.

 October 26, 2009, 19:39 #2 Senior Member   N/A Join Date: Mar 2009 Posts: 189 Rep Power: 10 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.

 October 27, 2009, 04:48 #3 Member   Newton KF Join Date: Mar 2009 Posts: 36 Rep Power: 10 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...

 October 27, 2009, 13:39 #4 Senior Member   N/A Join Date: Mar 2009 Posts: 189 Rep Power: 10 For diffusion you can use \mu * dt / dx^2 =0.5.

 October 27, 2009, 13:45 #5 Member   Newton KF Join Date: Mar 2009 Posts: 36 Rep Power: 10 Harishg, thanks for you reply... Can you indicate some papers that use this criterium??? thanks again...

 October 27, 2009, 14:18 #6 Senior Member   N/A Join Date: Mar 2009 Posts: 189 Rep Power: 10 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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