I am writing a code about unsteady compressible problem. I find if the time-step was set 10e-5,the program diverged. If it was set 10e-4,the program could converge. I want to set the time-step 10e-5. Can anyone give me some advice to make the program converge? Thanks a lot!

The stability criterion requires that U dt /dx and mu dt /dx^2 are less than certain values and hence in some cases lowering dt way too much might cause a problem with stability.

-H

No, too small a time step should not cause a problem! Most of the times it works to restrict dt according to the convective limit. It can, however, happen that the viscous terms become big enough to have an impact on the stability (very small cells, or very large viscosities)

dt = 0 could be a problem if you divide by it.

Vivian, can you give more details about your code? Explicit/implicit viscous/inviscid etc.?

My code follows the pressure-correction method solving the compressible problem. N-S equations are solved. I think it is semi-implicit and viscous.The working fluid is air.Amu is about 10e-5.