The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations

Bart  Janssens; Pierre  Vandenschrick; Kasper  Stevens; Giacomo  Alessi

doi:10.29008/ETC2019-242

13^th European Conference on Turbomachinery Fluid dynamics & Thermodynamics

Paper ID:

ETC2019-242

Main Topic:

Optimization

https://doi.org/10.29008/ETC2019-242

Authors

Bart Janssens - Royal Military Academy of Belgium
Pierre Vandenschrick - Belgian Defence
Kasper Stevens - Belgian Defence
Giacomo Alessi - von Karman Institute for Fluid Dynamics

Abstract

The finite element solution of the continuous adjoint to the Navier-Stokes equations requires stabilization similar to that required for the flow problem. This paper presents the stabilized adjoint equations and their boundary conditions, with the weak forms for the equations and boundary conditions. In addition to this, the weak form of the direct differentiation method is also presented. Finally, a test case using an S-shaped duct shows the agreement between the direct differentiation method and the adjoint method. Sensitivities and values of the adjoint solutions are given as validation data.