In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers” equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.
|Original language||English (US)|
|Title of host publication||46th AIAA Fluid Dynamics Conference|
|Publisher||American Institute of Aeronautics and Astronautics Inc, AIAA|
|State||Published - Jan 1 2016|