[c3k1uI5gzT]

Hi,

I am trying to implement a continuous adjoint formulation of the Spalart-Allmaras turbulence model. This comes down to programming three additional (adjoint) equations for the adjoint velocity, adjoint pressure, and the adjoint SA-variable. The first two are similar to the velocity and pressure equation with some minor modifications and work fine. The third is similar to the SA model transport equation.

My question is: What would be the most convenient way to implement this third equation, provided that
- it has a form similar to the SA model transport equation
- it uses both the velocity and the adjoint velocity
- it uses the SA coefficients/quantities

Proposed solution 1: implement it in a way similar to UEqn, pEqn, (as I did for UaEqn, paEqn for the other adjoint variables)
- difficulty: how to access the SA-quantities (e.g. fv1, fv2, coefficients, etc.) from the solver

Proposed solution 2: implement it in a way similar to the SA turbulence model, i.e. as a turbulence model
- difficulty: would require the use of two turbulence models/adjoint equation is not strictly a turbulence model

Thanks!

[c3k1uI5gzT]

For anyone wondering, I went for solution 2. I implemented the adjoint nuTilda equation in the same file as the nuTilda equation (spalartAllmaras.C). For the variables I needed which were not available in the turbulence model I used for example

this->db().objectRegistry::lookupObject<volVectorField> ("Ua");