[juanelo14]

Hi everybody, first of all I apologize for my english, it's not my first language.

I´m making my own code in Matlab for solving a Two Energy Equation Model (Porous media NTE) but i have a doubt about how to implement an outflow boundary condition for the fluid phase.

I´m working one dimensional flow in a very simple geometry, a square, the flow is in the x-direction.
I´m using the control volume method (Finite volume).
I´m using the power law scheme.

Remembering the general form of the control volume formulation:
aP*Tp=aE*TE+aW*TW+aN*TN+aS*Ts+b
aP=aE+aW+aN+aS-Sp*DX*DY+(Fe-Fw)*DY

My confusion lies in what it's satated in th Suhas Patankar´s book:

suppose the outflow boundary is the east boundary, Patankar states tha i should set the aE coeficient of the adyacent node to zero in order to eliminate the influence of the boundary node, and then let the value of the temperature be extrapolated from the upstream values.

according to what is stated above, should i just turn the aE coefficient to zero, and eliminate it's influence on aP or keep it.? And what about the boundary nodes, should i use the same aproach or should i use an extrapolation function (second order backward difference maybe?) or just stay stuck with the general formulation.


On the other hand, if i analyze the physical interpretation (or mathemathical) of the outflow boundary condition, it reduces, to assume the normal gradients of the flow variables (including temperature) are zero. Should i make a new discretization for the boundary node considering the above statement ?

I hope somebody can help me, thanks!!!