I'm trying to simulate a 3D model of the unsteady process of solidification/melt process of a PCM using a hot/cold fluid flow and i have a problem for determining the time step.
I've reached to some information that says the Courant number (CFL number) should be lower than a specific number for simulation to be accurate and stable.
Since the CFL number is C=u*delta_t/delta_x , is this statement true that with larger scales in geometry scales, i mean for example scaling the problem from millimeter to meter, the Courant number reduces and it allows the time step to be larger?
It should be noted that with larger scales both delta_x and U changes for the mesh element number and the Reynolds number to be equal to these specifications in smaller scales.
The delta_x increases in size and the U decreases for the Reynolds number to be the same.
So from theorical prespective C=u*delta_t/delta_x can be smaller by scaling the geometry?
Using explicit methods for convection-diffusion problems the stability constraint on the time step is not only due to the CFL condition but also on the diffusion parameter. You have to consider them simultaneously in the most critical region of the mesh.
Dear Farhad,
first, by changing the scale you don't get rid of the limitations. Just think of the CFL as of a nondimensional parameter of your simulation set-up. Second, as Filippo pointed out, if you examine a problem of thermofluid dynamics, there are other conditions besides CFL that can limit the time step of your simulation. The most important time step conditions can be found in this publication.
Article A Smoothed Particle Hydrodynamics Model for Laser Beam Melti...
https://www.sciencedirect.com/search?qs=effects%20of%20model%20geometrical%20scale%20on%20the%20transient%20time%20step&show=25&sortBy=relevance
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