Hello, I am new to cfd and I just try to understand the boundary condition of the epsilon in the page large fluid problem, the link is [large fluid problem] (https://doc.freefem.org/tutorials/aLargeFluidProblem.html)
the code is
89problem ViscosityTurbulence(ep, q)
90 = int2d(Th)(
91 (1.92epp/kp + alpha) * ep * q
92 + muT * grad(ep)’ * grad(q)
93 )
94 + int1d(Th, b1, b2)(
95 T * q * 0.001
96 )
97 + int2d(Th)(
98 prode * q
99 - alphaconvect([Upx, Upy], -dt, epp)q
100 )
101 + on(b5, b6, ep=0.00001)
102 + on(b1, b2, ep=betanuep*pow(stress,1.5))
103 ;
in the int1d part, what is the boundary condition of epsilon, that is ep,on b1,b2?
Note that strong form of the epsilon equation contains a viscous diffusion term (Laplacian). Hence, the term on line 92 was integrated by parts to get this weak form. Since there is no corresponding boundary integral, this imposes a Neumann condition on ep for any boundary without corresponding Dirichlet conditions (i.e. b3, b4).
The int1d term on line 95 is a boundary term that does not involve ep, hence it only appears in the RHS.
So, from what I can tell, we have homogeneous Neumann conditions along b3,b4 and inhomogeneous Dirichlet conditions on b1,b2,b5,b6.
Yes, that could be a correct BC in some applications, but it is not always the case. The author of that script chose Dirichlet/Neumann conditions for their problem, and apparently that was sufficient for their purpose.
If you want to implement a Robin BC, you can use, an int1d along your boundary of interest that enforces the Dirichlet part of the constraint. Note that the Neumann condition is already handled naturally via the elimination of the boundary term in the integration by parts.