Dear friends, One interesting question doesn't let me sleep for a long time. What's the rhole of Kurant's number (C=u*deltat/deltax) in building finite differences schemes? What happens when C==1 everywhere (I think I can make it)? Is this a stabilization(in stationary and non - stationary case) and what additional conditions do we have so that the scheme is stabilyzed? Does the number of Kurant have any influence in Finite Elements Method? Can the condition C==1 everywhere stabilyze any scheme in finite differences or finite elements methods that has good parameters, but is out of use, and what additional conditions do we have so that stabilization happens? Yours Mihail

Mihail,

First of all, you may return to sleep at nights ...

Courant number is a nondimensional number arising naturally when analyzing numerical schemes. Various schemes may have different critical Courant number, and this includes FDM, FVM and FEM.

Yes, but for most of the schemes C==1 makes the error due to scheme viscosity (in non- stationary case) equal to 0 (I mean the scheme backwards to flow and Lax scheme). This also improves the approximation of Navier - Stokes equation if looked at as a balance of accerelations (especially for the convective term).