I am studying the evolution of the density and velocity field of a core in a molecular cloud in 1 D.
I defined the radial grid (let us say x between 100 and 101) and the time grid.
I am using the finite element method which is very unstable. Now I need to use the CFL condition, so I must find the suitable time step and x step, or else my algorithm becomes heavily unstable and the results blow up.
I don't really understand how to find the velocity in the CFL condition, since x is increasing, and the time is changing, this means that the velocity (=x/time) is changing at each step right? so will I need to change the CFL condition at each iteration?

  • $\begingroup$ You'll have to recompute the stable timestep size for each timestep. $\endgroup$ – Biswajit Banerjee Feb 14 at 20:20

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