# Navier Stokes with very small time steps

**URL:** <https://community.freefem.org/t/navier-stokes-with-very-small-time-steps/4082>\
**Category:** General Discussion\
**Created:** [September 26, 2025, 5:43pm UTC](https://community.freefem.org/t/navier-stokes-with-very-small-time-steps/4082 "2025-09-26T17:43:42Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Arun](https://avatars.discourse-cdn.com/v4/letter/a/ee7513/32.png) [@Arun](https://community.freefem.org/u/Arun)\
**Post date:** [September 26, 2025, 5:43pm UTC](https://community.freefem.org/t/navier-stokes-with-very-small-time-steps/4082/1 "2025-09-26T17:43:42Z")

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Hello,

I am trying to solve incompressible transient Navier Stokes equation using very small time steps. I have tried the examples given in the documentation including the projection and NS Uzawa Cahouet Chabart solvers. However if I make the time step smaller than the ones given in those examples solution becomes either unstable or spurious errors emerge. I don’t have much experience with NS. Any help and guidance regarding which type of formulation will be suitable for problems with small time steps will be appreciated. Thanks.

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**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [October 3, 2025, 9:34am UTC](https://community.freefem.org/t/navier-stokes-with-very-small-time-steps/4082/2 "2025-10-03T09:34:52Z")

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The non linear term in exemple [FreeFem-sources/examples/tutorial/NSUzawaCahouetChabart.edp at develop · FreeFem/FreeFem-sources · GitHub](https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/tutorial/NSUzawaCahouetChabart.edp)

the non linear term use the characteristic method, and long time ago S. Piperno show that the method do not converge if the time step go to 0.

So I think you see this.