Comparison of two adjoint equation approaches with respect to boundary-condition treatment for the quasi-1D Euler equations

For computation of nonlinear aeroelastic problems, an efficient error estimation and grid adaptation algorithm is highly desirable, but traditional error estimation or grid adaptation do not suffice, since they are insufficiently related to relevant engineering variables and are incapable of significantly reducing the computing time. The dual formulation however, can be used as an a-posteriori error estimation in the quantity of interest. However, derivation of the dual problem, especially the accompanying boundary conditions, is not a trivial task. This document compares a discrete and analytical ad joint equation method with respect to boundary-condition treatments applied on the quasi-1D Euler equations. Flux evaluation of the primal problem is do ne by a Linearised Godunov scheme. For our future goal, solving ftuid-structure problems, the discrete approach seems preferable.