# Periodic mesh advection

**URL:** <https://community.freefem.org/t/periodic-mesh-advection/3612>\
**Category:** General Discussion\
**Created:** [December 3, 2024, 2:28pm UTC](https://community.freefem.org/t/periodic-mesh-advection/3612 "2024-12-03T14:28:18Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![quentin](https://avatars.discourse-cdn.com/v4/letter/q/e47c2d/32.png) [@quentin](https://community.freefem.org/u/quentin)\
**Post date:** [December 3, 2024, 2:28pm UTC](https://community.freefem.org/t/periodic-mesh-advection/3612/1 "2024-12-03T14:28:18Z")

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How to track a moving Lagrangian boundary with L-periodic in x direction?

I know such problem is solved by Alan Riquier,

[Numerical study of a viscous breaking water wave and the limit of vanishing viscosity](https://doi.org/10.1017/jfm.2024.208)

> **[05\_slides\_canum\_05\_2024.pdf](https://www.math.ens.psl.eu/~ariquier/documents/presentations/05_slides_canum_05_2024.pdf)**
>
> 19.51 MB

 ![p1](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/5/5b6566dab1bc1688490db21af26f9e6c5704cc48.png)

 ![p2](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/f/f49a9aa574c7bef77b98a74359f95576286b50f9.png)  
In slide p2, the advected mesh seems to be related to `movemesh` :

```auto
mesh th1 = movemesh(Th, [x+w1*coef, y+w2*coef])

```

However I am not sure how to do this with a pair of periodic boundary. The difficulty to ensure that the geometry shape is unchanged except for the moving interface. And, how to to deal with upper-left and upper right vertices?

Unfortunately, the paper didn’t show details of the numerical implementation.  
Does anyone know how to reproduce it?

Best regards.