Use of the Adjoint Method to Assess the Error in Simulations

In this work, a sensitivity calculation approach called the adjoint method is explored to estimate and control the discretization error in computational fluid dynamic (CFD). This paper describes how the adjoint is applied to incompressible RANS simulations to approach the continuous solution which is unknown. While the adjoint method is already widespread in aerodynamics to optimize designs, here it is used as an error estimator. The error is thus calculated from the scalar product of sensitivities to an objective function selected by the user (efficiency, power, losses, etc.) with respect to residuals of governing equations. The key point is that adjoint method pinpoints the sensitive areas of the simulation. By adapting the mesh accordingly, it is possible to improve the numerical accuracy while keeping the mesh size manageable.