<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The optimal control of moving boundary problems receives growing attention in science and technology. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. The Stefan problem is coupled with incompressible Navier{Stokes equations. We take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state and the control costs. With the formal Lagrange approach and an adjoint system we derive the gradient of the cost functional. The derived formulations can be used to achieve a desired interface position. Among others, we address how to handle the weak discontinuity of the temperature along the interface with mesh movement methods in a finite element framework.</p></abstract>

The optimal control of moving boundary problems receives growing attention in science and technology. We consider the so called two-phase Stefan problem that models a solid and a liquid phase separated by a moving interface. The Stefan problem is coupled with incompressible Navier{Stokes equations. We take a sharp interface model approach and define a quadratic tracking-type cost functional that penalizes the deviation of the interface from the desired state and the control costs. With the formal Lagrange approach and an adjoint system we derive the gradient of the cost functional. The derived formulations can be used to achieve a desired interface position. Among others, we address how to handle the weak discontinuity of the temperature along the interface with mesh movement methods in a finite element framework.

Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes Equations and Mesh Movement

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The optimal control of moving boundary problems receives growing attention in science and technology. We consider the so called two-phase Stefan problem that...

Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes Equations and Mesh Movement

Published Online: Nov 22, 2018

Page range: 11 - 40

Received: Mar 01, 2017

Accepted: Jun 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0016

Keywords
Stefan problem, optimal control, moving interface, mesh movement, Navier- Stokes equations.

© 2018 Bjőrn Baran, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Optimal Control of a Stefan Problem Fully Coupled with Incompressible Navier-Stokes Equations and Mesh Movement

Published Online: Nov 22, 2018

Page range: 11 - 40

Received: Mar 01, 2017

Accepted: Jun 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0016

KeywordsStefan problem, optimal control, moving interface, mesh movement, Navier- Stokes equations.

© 2018 Bjőrn Baran, et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Stefan problem, optimal control, moving interface, mesh movement, Navier- Stokes equations.