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

B. Janssens; P. Vandenschrick; K. Stevens; G. Alessi

doi:10.29008/etc2019-242

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

B. Janssens, P. Vandenschrick, K. Stevens, G. Alessi

Fluid Dynamics

Von Karman Institute for Fluid Dynamics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	Undefined/Unknown
Title of host publication	Proc. of the 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics
Pages	1-12
Number of pages	12
Edition	2015
DOIs	https://doi.org/10.29008/etc2019-242
Publication status	Published - 2019

Publication series

Name	13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019

Access to Document

10.29008/etc2019-242

Cite this

Janssens, B., Vandenschrick, P., Stevens, K., & Alessi, G. (2019). The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations. In Proc. of the 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics (2015 ed., pp. 1-12). (13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019). https://doi.org/10.29008/etc2019-242

Janssens, B. ; Vandenschrick, P. ; Stevens, K. et al. / The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations. Proc. of the 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics. 2015. ed. 2019. pp. 1-12 (13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019).

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

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.",

keywords = "Continuous adjoint method, Finite element method, Incompressible flow, Optimization",

author = "B. Janssens and P. Vandenschrick and K. Stevens and G. Alessi",

year = "2019",

doi = "10.29008/etc2019-242",

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series = "13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019",

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Janssens, B, Vandenschrick, P, Stevens, K & Alessi, G 2019, The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations. in Proc. of the 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics. 2015 edn, 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019, pp. 1-12. https://doi.org/10.29008/etc2019-242

The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations. / Janssens, B.; Vandenschrick, P.; Stevens, K. et al.
Proc. of the 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics. 2015. ed. 2019. p. 1-12 (13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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Janssens B, Vandenschrick P, Stevens K, Alessi G. The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations. In Proc. of the 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics. 2015 ed. 2019. p. 1-12. (13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2019). doi: 10.29008/etc2019-242