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

Sameh Abidi; Jamil Satouri; Sameh Abidi; Jamil Satouri

doi:10.3934/math.20231095

AIMS Mathematics

2023, Volume 8, Issue 9: 21484-21500. doi: 10.3934/math.20231095

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

Sameh Abidi ^{1,2
,
,},
Jamil Satouri ^{3
,
,}

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

Received: 03 March 2023 Revised: 23 May 2023 Accepted: 25 May 2023 Published: 05 July 2023
MSC : 76B75, 76D55

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.
- optimal control,
- Navier-Stokes equations,
- spectral method,
- optimization
Citation: Sameh Abidi, Jamil Satouri. New numerical method for solving optimal control problem for the stationary Navier-Stokes equations[J]. AIMS Mathematics, 2023, 8(9): 21484-21500. doi: 10.3934/math.20231095

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Abstract

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.

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