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"... 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 equi ..."
Abstract
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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 dif � culties associated with the use of linear perturbation and adjoint methods for applications with strong shocks are also examined. Nomenclature B = boundary condition projection operator I.z / = imaginary part of complex variable z i = p ¡1 J = nonlinear output functional, for example, lift QJ = linear perturbation to functional L = linearized discrete operator R = nonlinear discrete residual operator U = nonlinear variables u = linear perturbation variables v = adjoint variables ® = design/sensitivity variable Subscripts? = orthogonal to boundary conditions k = parallel to boundary conditions Superscripts.m / = subiteration index n = iteration index T = transpose
