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-   -   How to implement Robin Boundary Conditions? (http://www.cfd-online.com/Forums/main/112974-how-implement-robin-boundary-conditions.html)

 giorgk February 8, 2013 18:36

How to implement Robin Boundary Conditions?

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

 FMDenaro February 9, 2013 04:52

Quote:
 Originally Posted by giorgk (Post 406813) 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.

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