Algorithm developments for discrete adjoint methods

A number of algorithm developments are presented for adjoint methods using the "discrete" approach in which the discretization of the nonlinear equations is linearized and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equations, exact numerical equivalence is maintained between the linear and adjoint discretizations. The incorporation of strong boundary conditions within the discrete approach is discussed, and difficulties associated with the use of linear perturbation and adjoint methods for applications with strong shocks are also examined.