Adjoint based optimisation of reactive compressible flows

We derive adjoint equations for the reactive compressible Navier–Stokes equations. Therein the reaction rate is modelled by an Arrhenius approach. The adjoint equations are validated by means of a comparison between the adjoint solution and a finite difference expression. An adjoint based optimisation framework for reactive compressible flows is presented. Formulations for different target functions are shown. One- and two-dimensional laminar flame configurations are presented. We find, that the adjoint approach works well despite the strong non-linearity of the reaction terms.