How to apply this unique Mix of Neuman + Dirichlet Boundary conditions, for Temperature & Pressure, 1-d Problem

Mikey Hannon 

The Neuman BC on the left side is OK, but I'm not sure the Dirichlet condition for P and Neuman condition for T can be both obtained by adding a large (inactive) element with conditions equal to the initial ones.

This is OK for the P BC, which will be held at the initial constant value,  P=Po.

But this choice will enforce the same boundary condition (Dirichlet) for the T too. To suppress the heat conduction the thermal conductivity of the rock domain to which the inactive boundary element belongs should be set to zero. Depending on the interpolation method used by the code for the thermal conductivity along a connection, it could be necessary to set to zero also the thermal conductivity of the last element on the right boundary of the 1D linear grid.

If the T changes within the 1D grid, the T derivative dT/dx along the last right connection will not be necessarily zero, but there will be no heat conduction because of the heat conductivity assignment. 

Alfredo Battistelli , I've also been thinking this over some, too.  I did think of setting the thermal conductivity to zero to suppress heat conduction, but convection would still go on unabated, correct? 

Mikey Hannon Sure, flow would not be inhibited through the right boundary. If fluid flux is going outside of the system with no conduction,  the BC for T should be close to Neuman.

I have some doubt if fluid flux is entering the system from the right boundary.

Alfredo Battistelli I agree, but you would still have fluid exiting the system, so it's not perfect. telegramboy I would suggest following Alfredo's suggestion and assign a zero thermal conductivity to the large element boundary.  If you keep the node distance small, it should make the thermal conductivity of the connection (boundary) zero as well.  That'll get you closer to the boundary conditions you're looking for.

Mikey Hannon 

 a. Fluid exiting the system cannot be avoided, as it is a consequence of the constant P boundary condition.

b. Using a short node distance from the interface for the inactive element is necessary to have the const P boundary at the right place, but it should  not affect the interpolation of the thermal conductivity. I do not know  what is done in the specific code used, but in TOUGH2 the thermal conductivity along the connection  is weighted considering the fractional lenght of each nodal distance. So, it should be necessary to assign zero thermal conductivity on both the last element on the right boundary and in the inactive element. A small active element on the right boundary could be added and used for this purpose.