Efficient adaptation using discrete adjoint error estimates in unsteady flow problems

This paper presents a framework for the reduction of the spatial, temporal and algebraic error by use of the discrete adjoint solution 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 efficient manner. A simple unsteady problem of a vortex convecting through a time integrated box is used to demonstrate that the frequency of reflnement has a large impact on the overall computational efficiency of the solution. Analysis of the simplified problem shows that adaption of one parameter in isolation results in a limited improvement in accuracy and a combination of adapting on the three types of error is necessary to get any significant improvement. A method is developed to address this restriction and tested. The improved efficiency of the new method is demonstrated on the simplified test problem and an additional test case of a vortex convecting past an airfoil.