New numerical method for solving optimal control problem for the stationary Navier-Stokes equations-Reference-Cited by-同舟云学术

New numerical method for solving optimal control problem for the stationary Navier-Stokes equations

Published:2023 Issue:9 Volume:8 Page:21484-21500
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Abidi Sameh¹²,Satouri Jamil³

Affiliation:

1. Department of Management Information Systems, College of Business Administration, Qassim University, Al-Rass, Al-Qassim, Saudi Arabia

2. UR22ES12: Modeling Optimization and Augmented Engineering, ISLAIB, University of Jendouba, Béja 9000, Tunisia

3. Al-Qunfudah University College, Umm Al-Qura University, Al-Qunfudah, Mecca, Saudi Arabia

Abstract

<abstract><p>The purpose of this article is to propose a new numerical method to solve the problem of optimal control of the steady-state Navier-Stokes equations via the velocity-pressure formulation. We apply a new technique to derive a system of equations from which the solution can be calculated. The spectral method is used to discretize the problem. An extended relaxation method is proposed in the numerical part to ensure the correct convergence of the system. Finally, numerical results are provided to confirm the effectiveness of this approach.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference26 articles.

1. V. Isakov, Inverse problems for partial differential equations, New York: Springer, 1998. https://doi.org/10.1007/978-1-4899-0030-2

2. M. Kern, Problèmes inverses aspects numériques, Engineering school. 1999 à 2002, École supérieure d'ingénieurs Léonard de Vinci, 2002, cel-00168393v2.

3. S. El Yacoubi, J. Sokołowski, Domain optimization problems for parabolic control systems, Appl. Math. Comput. Sci., 6 (1996), 277–289.

4. A. Henrot, J. Sokołowski, A shape optimization problem for the heat equation, In: Optimal control, Boston, MA: Springer, 1998,204–223. https://doi.org/10.1007/978-1-4757-6095-8_10

5. K. H. Hoffmann, J. Sokołowski, Interface optimization problems for parabolic equations, Control Cybernet, 23 (1994), 445–451.