Verification of an Adjoint Code for FGM Combustion

The adjoint method efficiently computes the sensitivity of a global output objective function, such as a combustor outlet temperature uniformity or NOx emission, with respect to a large number of input design variables, such as the centroids of the wall boundary faces. This sensitivity gradient can be used in an optimization algorithm, in particular for shape or topology design to extremize the objective function. In this work, the adjoint model in Simcenter STAR-CCM+ is extended to the Flamelet Generated Manifold (FGM) combustion model. The discrete adjoint is solved by differentiating the linearized flow solver using Automatic Differentiation, transposing these operations, and executing the code in the reverse order. Since the code is complex with a large number of interacting models, a careful verification is required to ensure that the important parts of the code are differentiated properly, and the order of code execution is correct. A global sensitivity for a simple mixing layer flame is compared for forward derivatives (tangent mode), reverse derivatives (adjoint mode) and finite differences. Despite vastly different code path execution for adjoint, tangent and finite-difference, the close agreement of various objective function calculations verifies the correct implementation of the adjoint and tangent code.