Hi, I just was wondering what makes implicit solvers more stable as compared with explicit ones in terms of CFL number.. Cheers endee

This can be answered on so many levels, but it's such a basic question that almost any textbook on CFD will give you an answer. The CFL condition basically states that within any explicit time step, flow information is not allowed to propagate farther than from one grid point to the adjacent grid point. Given a grid and flow, this condition provides a maximum limit for the time step.

The exact stability condition will depend on the numerical scheme, and for linear equations you can find it by a von Neumann stability analysis as described in your textbook. The same stability analysis on implicit schemes will reveal that they are more stable (even unconditionally stable). You could argue that the reason is given by the implicit connection of all grid points in such schemes. In explicit schemes only the immediate neighbors (within the stencil) exchange information within each time step. Hence the CFL condition. With implicit schemes, the connectivity ideally reaches through the entire grid.