Imbedded Dual-Number Automatic Differentiation to Support CFD Analysis

Dual number automatic differentiation was applied to two different computational fluid dynamics codes, one written specifically for this purpose and one larger “legacy” Fortran code. Results for the simple case of a fully developed laminar flow in a channel validated the accuracy of the approach in computing derivatives with respect to both a fluid property, and a geometric dimension. DNAD was also implemented into the JET Fortran program which is available with a popular turbulence modeling textbook as companion software. Mean centerline velocity derivatives for a self-similar round jet with respect to all applicable turbulence model closure coefficients for both k–ω and k–ε models were obtained. The method proved to be accurate and relatively simple to implement into both the new and legacy Fortran codes.