Watch Your Adjoints! Lack of Mesh Convergence in Inviscid Adjoint Solutions

Abstract: It has been long known that 2D and 3D inviscid adjoint solutions are generically singular at sharp trailing edges. In this paper, a concurrent effect is described by which wall boundary values of 2D and 3D inviscid continuous and discrete adjoint solutions based on lift and drag are strongly mesh dependent and do not converge as the mesh is refined. Various numerical tests are performed to characterize the problem. Lift-based adjoint solutions are found to be affected for any flow condition, whereas drag-based adjoint solutions are affected for transonic lifting flows. A (laminar) viscous case is examined as well, but no comparable behavior is found, which suggests that the issue is exclusive to inviscid flows. It is argued that this behavior is caused by the trailing edge adjoint singularity.