Vaggelis Papoutsis authored Feb 07, 2022 and Andrew Heather committed Jun 10, 2022

for incompressible flows. The typical convention of appending the primal
field name with 'a' to form the adjoint field is followed for the
adjoint turbulent kinetic energy (i.e. 'ka') but since this would produce
an ugly variable name for the adjoint to omega (i.e. omegaa), the latter
is abbreviated to 'wa'.

The work is based on

\verbatim
    Kavvadias, I., Papoutsis-Kiachagias, E.,
    Dimitrakopoulos, G., & Giannakoglou, K.  (2014).
    The continuous adjoint approach to the k–$omega$ SST turbulence model with
    applications in shape optimization
    Engineering Optimization, 47(11), 1523-1542.
    https://doi.org/10.1080/0305215X.2014.979816
\endverbatim

with changes in the discretisation of
a number of differential operators and the formulation of the adjoint to
the wall functions employed by the primal model.

Regarding the latter, the code assumes (and differentiates) the default
behaviour of nutkWallFunction (i.e. nutWallFunction::blendingType::STEPWISE)
and omegaWallFunction (i.e. omegaWallFunction::blendingType::BINOMIAL2).

Due to the availability of a number of terms required for the
formulation of the wall function for ka, the latter is implemented
within adjointkOmegaSST itself, with contributions from objective functions
implemented within kaqRWallFunction. Wall functions for wa are
implemented within waWallFunction.

The initial implementation of the above-mentioned reference was
performed by Dr. Ioannis Kavvadias