Dividing variational equation by time step in Navier Stokes example

General
1

Is there a specific reason why in this Fenics example for Navier Stokes equations, in the 3d step of the splitting scheme, the variational equations have been multiplied by the time step \Delta t

L3= dot(u_, v)*dx - k*dot(nabla_grad(p_ - p_n), v)*dx ?

Note that in the code \Delta t is equal to k.

Is this because keeping \Delta t in the denominator introduces some numerical instability?

Thank you

2

If dt->0 the matrix entries goes to infinity, while if you multiply by dt u=u_n-1.

So yes, you avoid potential numerical issues.

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