Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver

The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by \citet{Mader:2008:B}. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier--Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD.MAS