Courant number

##### Title

##### Question

Hi dear staff, i saw in the video the courant number was over the 1, 3.367 i would like if this number affect the simulation, because i know that the courant number would be less than 1.

Thanks you

OpenFOAM Turbulent-Flow-in-a-Lid-driven-Cavity 06-07 min 30-40 sec

__Answers:__

Hey,

So in a simulation where the time stepping scheme is explicit, like Forward Euler, we have a Courant Number condition of being less than 1. But OpenFOAM time stepping schemes are implicit and thus the Courant Number condition is relaxed. Thus for implicit schemes, Courant number can be above 1, but it still has some upper bound to preserve stability.

So in a simulation where the time stepping scheme is explicit, like Forward Euler, we have a Courant Number condition of being less than 1. But OpenFOAM time stepping schemes are implicit and thus the Courant Number condition is relaxed. Thus for implicit schemes, Courant number can be above 1, but it still has some upper bound to preserve stability.

The maximum Courant number that is permissible depends on the stability of our governing equations. Governing differential equations can be solved using two different temporal numerical schemes.

1) Explicit

2) Implicit

Courant No. < 1 is a strict restriction when using explicit solution approach. For higher value, this approach leads to unstable diverging solutions. However, this condition can be relaxed in case of implicit approach and higher Courant number can also give stable solution.

The maximum permissible Courant no. in case of implicit numerical scheme depends on problem specifications.

However, Courant No <1 is stable criteria for all schemes and hence it is advisable to follow this for simpler problems where computational times are low.

1) Explicit

2) Implicit

Courant No. < 1 is a strict restriction when using explicit solution approach. For higher value, this approach leads to unstable diverging solutions. However, this condition can be relaxed in case of implicit approach and higher Courant number can also give stable solution.

The maximum permissible Courant no. in case of implicit numerical scheme depends on problem specifications.

However, Courant No <1 is stable criteria for all schemes and hence it is advisable to follow this for simpler problems where computational times are low.

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