Discrete adjoint based adaptive error control in unsteady flow problems

This paper presents a framework for the estimation of spatial, temporal and algebraic error in a time integrated functional (i.e. Lift, Drag, etc.) for problems of aerodynamic interest. The three types of error are separated into distinct contributions that are used to selectively adapt the discretization to reduce the error in the functional in the most eficient manner. A simple unsteady test case is used to demonstrate that the individual components of error can be separated out and properly account for the error in the calculated objective. Adaption of convergence tolerance, time step size and grid resolution are shown to reduce computational expense while improving the accuracy of the functional of interest.