A note on the dual consistency of the discrete adjoint quasi-one-dimensional Euler equations with cell-centered and cell-vertex central discretizations

• Dual consistency of a central finite-volume scheme for the quasi-1D Euler equations is examined.
• The cell-vertex discretization is dual consistent, but the cell-centered one is not.
• The cell-centered discrete adjoint solution shows oscillations near the boundaries.

A flow discretization is dual-consistent if the associated discrete adjoint equations are consistent with the analytic adjoint equations. We examine here the formulation and numerical solution of the discrete adjoint quasi-one-dimensional Euler equations derived from a second-order, central-difference, finite volume scheme, for both cell-centered and cell-vertex discretizations. It is shown that, while the cell-vertex discretization is dual-consistent, the cell-centered discretization is not, showing oscillations near the boundaries.