[Islem]

Hi foamers,

I would like to compute the concentration field in order to determine the source term parameters. For this I need to implement the adjoint equation of the scalar transport equation. I am using openfoam V12.

The difference between the forward equation (convective-diffusive equation) and the adjoint equation is that the temporal and convective terms of the adjoint equation are apposite in signs to those of the forward equation and also the time sequence is inverted (see attached image for more details, C and C* represent the concentration field obtained from the forward and adjoint equations respectively, K(x,t) is the diffusion coeffcient, RHS of the equation represents the source).

My questions are:

1) Is this kind of adjoint equation of the the scalar transport equation already implemented in OpenFoam?

2) If no, any help regarding how to implement the equation. Any materials already available?? I am stuck, and don't know how to start.

3) How to implement the boundary conditions of the adjoint equation.

Any help/ hints would be very much appreciated.

Regards,
Islem