In this research, a framework based on the discrete adjoint method is presented for evaluating the sensitivities of a set of parameters related to chemically reacting flows. The presented formulation is implemented to laminar, incompressible regimes with constant density. The discrete adjoint formulation demands the solution of two sets of equations, namely the flow (primal) equations and the adjoint (dual) equations. The flow equations consisting of a coupled system of three models, namely fluid flow, thermal energy transfer and species mass transfer, are discretized using the stabilized finite element formulation while an implicit scheme is implemented to solve the discretized equations. The adjoint equations including a coupled linear system of equations employ the transpose of the exact Jacobian matrices, incompletely calculated for the implicit solution of the flow equations. The coupled systems of equations deduced from both the flow and the adjoint equations are solved in a staggered manner while a highly-parallel preconditioned scheme for fractional solvers' with high scalability properties is employed. Some two-dimensional examples corresponding to the sensitivity analysis of a set of parameters are delivered here for the uncoupled as well as the coupled problems. The comparison of the calculated sensitivities with the ones obtained from the finite difference proves the accuracy and robustness of the proposed method.
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