# Traction on the outflow boundary

**URL:** <https://community.freefem.org/t/traction-on-the-outflow-boundary/2167>\
**Category:** General Discussion\
**Created:** [December 5, 2022, 10:13am UTC](https://community.freefem.org/t/traction-on-the-outflow-boundary/2167 "2022-12-05T10:13:24Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![gnaganlu](https://avatars.discourse-cdn.com/v4/letter/g/cdc98d/32.png) [@gnaganlu](https://community.freefem.org/u/gnaganlu)\
**Post date:** [December 5, 2022, 10:13am UTC](https://community.freefem.org/t/traction-on-the-outflow-boundary/2167/1 "2022-12-05T10:13:25Z")

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I am studying about the identification of immersed obstacles in fluid flows by using a traction vector (stress vector) on the boundary as an inverse problem procedure. The domain is rectangular and the right edge is the outflow boundary. At this outflow boundary sigma(u,p).n=0  
I just want to ask you about the traction vector(sigma). I want to correct that on the outflow-boundary this traction vector is exactly zero. All traction vectors are zero on the whole boundary in my freefem++ if I write the boundaries as follows.  
trac1xneg=int1d(Th,1)(-Mu\*(dx(uy)+dy(ux)));( First component of traction vector on bottom)  
trac2xneg=int1d(Th,1)(p-2_Mu_(dy(uy))); (Second component of traction vector on bottom)  
trac1ypoz=int1d(Th,3)(-p+2_Mu_(dx(ux))); (fist component of the traction vector on outflow)  
trac2ypoz=int1d(Th,3)(Mu\*(dx(uy)+dy(ux))); (second component of the traction vector on outflow)  
trac1xpoz=int1d(Th,1)(Mu\*(dx(uy)+dy(ux)));( First component of traction vector on top)  
trac2xpoz=int1d(Th,1)(-p+2_Mu_(dy(uy))); (Second component of traction vector on top)  
trac1yneg=int1d(Th,2)(p-2_Mu_(dx(ux))); (First component of traction vector on inlet)  
trac2yneg=int1d(Th,2)(-Mu\*(dx(uy)+dy(ux)));(Second component of traction vector on inlet)

If I define it as a function, the traction vector on outflow and also other boundaries is nonzero.

func trac1xneg=-Mu\*(dx(uy)+dy(ux));  
func trac2xneg=p-2_Mu_(dy(uy));  
func trac1ypoz=-p+2_Mu_(dx(ux));  
func trac2ypoz=Mu\*(dx(uy)+dy(ux));  
func trac1xpoz=Mu\*(dx(uy)+dy(ux));  
func trac2xpoz=-p+2_Mu_(dy(uy));  
func trac1yneg=p-2_Mu_(dx(ux));  
func trac2yneg=-Mu\*(dx(uy)+dy(ux));

Could you give me a suggestion to correct that traction is exactly zero on the just outflow boundary? How can I show it?

Thank you