TY - JOUR
T1 - The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations
AU - Janssens, B.
AU - Vandenschrick, P.
AU - Stevens, K.
AU - Alessi, G.
N1 - Publisher Copyright:
Copyright © by the Authors.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Continuous adjoint method
KW - Finite element method
KW - Incompressible flow
KW - Optimization
UR - http://www.scopus.com/inward/record.url?scp=85199012549&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85199012549
SN - 2313-0067
JO - European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC
JF - European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC
T2 - 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019
Y2 - 8 April 2019 through 12 April 2019
ER -