# How to implement Robin Boundary Conditions?

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 February 8, 2013, 18:36 How to implement Robin Boundary Conditions? #1 New Member   Join Date: Feb 2013 Posts: 3 Rep Power: 6 Hi, I'm currently working with a code that requires to assign the Boundary conditions using the coefficients on the general form of Robin Bc (a*u + b * du/dn = g) From my understanding I can assign Dirichlet conditions by setting a=1, b=0, and g the desired specified value. Similarly for Neuman bc I need to set a=0, b=1, and g the desired value. is this correct so far? Now lets considered a quadrilateral element 1--------2 | | | | 3--------4 where there is Neuman boundary defined over the element and dirichlet on the nodes 1 and 3 Since I'm doing groundwater modeling, lets say I have specified hydraulic head for nodes 1 and 3 H=10 m and recharge flux equal to 1e-4 m/day. Lets say that the area of the element is 1e6, then 100 m^3/day are coming into that element. Using FE discretization the flux will split into 25 m^2/day per node. I assume that for the nodes 2 and 4 the coefficients have to be a=0, b=1, g=25. But what are the values for the nodes 1 and 3? Thank you George

February 9, 2013, 04:52
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by giorgk Hi, I'm currently working with a code that requires to assign the Boundary conditions using the coefficients on the general form of Robin Bc (a*u + b * du/dn = g) From my understanding I can assign Dirichlet conditions by setting a=1, b=0, and g the desired specified value. Similarly for Neuman bc I need to set a=0, b=1, and g the desired value. is this correct so far? Now lets considered a quadrilateral element 1--------2 | | | | 3--------4 where there is Neuman boundary defined over the element and dirichlet on the nodes 1 and 3 Since I'm doing groundwater modeling, lets say I have specified hydraulic head for nodes 1 and 3 H=10 m and recharge flux equal to 1e-4 m/day. Lets say that the area of the element is 1e6, then 100 m^3/day are coming into that element. Using FE discretization the flux will split into 25 m^2/day per node. I assume that for the nodes 2 and 4 the coefficients have to be a=0, b=1, g=25. But what are the values for the nodes 1 and 3? Thank you George

Assume the point 3 is at x=y=0 coordinates. Assume a bi-linear approximation on 1-2-3-4:

u(x,y) = c0 + c1*x +c2*y +c3*xy

that over the boundary x=0 leads to

du/dx = c1+c3*y

Hence, your Robin Bc along edge 3-1 becomes

a*(c2*y) + b*(c1+c3*y)= g

where a,b, g must be known from your problem.

 June 12, 2017, 10:40 How to implement Robin Boundary Conditions in groovy? #3 New Member   Sachin Join Date: Sep 2016 Location: Poitiers,France Posts: 17 Rep Power: 2 Hello, I also would like to implement robin boundary condition in my electrostatic program. To implement my robin BC in code, I am comparing my problem with heat exchange robin BC. Final robin BC in heat exchange problem is Tface = f*Tinf + (1-f)* Tcentre ; f=(1+(k/alpha*delta)) So my question is how to find fraction value (f) in robin BC? My robin BC is (E*Np)-(grad*Np)=0 Here E is surfaceScalarField ; Np is volScalarField(both scalar value I am calculate). So can anyone help me to find out fraction value for robin boundary condition and how to implement in groovy? Thanks

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