# Implement a force-free condition

**URL:** <https://community.freefem.org/t/implement-a-force-free-condition/2041>\
**Category:** General Discussion\
**Created:** [October 5, 2022, 3:10am UTC](https://community.freefem.org/t/implement-a-force-free-condition/2041 "2022-10-05T03:10:18Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![zhugp123](https://avatars.discourse-cdn.com/v4/letter/z/71e660/32.png) [@zhugp123](https://community.freefem.org/u/zhugp123)\
**Post date:** [October 5, 2022, 3:10am UTC](https://community.freefem.org/t/implement-a-force-free-condition/2041/1 "2022-10-05T03:10:18Z")

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I know how to solve the diffusion-convection equation for concentration and Stokes equation in FreeFem++, but I have no idea about implementing the force-free condition to obtain **U**. Can anyone give me some suggestions on implementing the force-free condition? Does FreeFem++ have similar examples? I would appreciate any help you give me.

 ![Governing_Equation](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/7/73cabc1cd8fb2bcec0f12e932e2f6c4e12b5a602.png)

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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 5, 2022, 6:57am UTC](https://community.freefem.org/t/implement-a-force-free-condition/2041/2 "2022-10-05T06:57:57Z")

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This is simple, put no boundary condition on this part of the boundary.

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**Author:** ![zhugp123](https://avatars.discourse-cdn.com/v4/letter/z/71e660/32.png) [@zhugp123](https://community.freefem.org/u/zhugp123)\
**Post date:** [October 5, 2022, 8:54am UTC](https://community.freefem.org/t/implement-a-force-free-condition/2041/4 "2022-10-05T08:54:42Z")

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Dear Prof. Frédéric Hecht,  
Thanks for your kind reply. I may not make the question clear. The force-free condition (marked in blue in the above question) is imposed on the particle \Gamma\_p (the total hydrodynamic force exerted on the particle is zero). The outer boundary \Gamma\_o is the negative translation velocity \mathbf{U} (in the particle frame). Note that \mathbf{U} is unknown and it is determined iteratively by requiring that the total hydrodynamic force (force-free condition) on the particle surface \Gamma\_p is zero at all times.  
 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/4/41dba8a67ece49f8afc7d90f0b4ad165749c2805.png)