Sensitivity analysis of one-dimensional mixed initial-boundary value problems: Application to freely propagating premixed laminar flames

A procedure for calculating sensitivity coefficients of one-dimensional parabolic mixed initial-boundary value problems is developed. The method is based upon the use of implicit time integration and Newton's method in solving the governing equations. The link between the sensitivity coefficients and the solution method is studied with particular emphasis on the use of adaptive gridding and variable time stepping. The method is employed in the analysis of two model freely propagating premixed laminar flames. The numerical accuracy of the sensitivities is verified and their values are utilized for interpretation of the model results.