Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

Satouri, Jamil

doi:10.1515/jiip-2016-0084

Journal of Inverse and Ill-Posed Problems

2018

DOI: 10.1515/jiip-2016-0084

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Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

Jamil Satouri

Abstract: In this paper we present a study of optimal control problem for the unsteady Navier–Stokes equations. We discuss the existence of the solution, adopt a new numerical resolution for this problem and combine Euler explicit scheme in time and both of methods spectral and finite elements in space. Finally, we give some numerical results proving the effectiveness of our approach.

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2023

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Cited by 2 publications

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Effect of V-Shaped Groove Microstructure on Blood Flow Resistance in Bionic Artificial Blood Vessels

et al. 2023

Applied Bionics and Biomechanics

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This study aims to investigate the blood flow in bionic artificial blood vessels and to reduce the resistance to blood flow, the drag reduction characteristics of V-shaped groove drag reduction microstructures in artificial blood vessel structures were investigated in depth. By varying the parameters of incoming flow velocity, groove width, and groove depth, the effect of various variable conditions on the drag reduction effect of the grooves was investigated, and the flow field characteristics and drag reduction effect of the V-shaped groove microstructure in the artificial blood vessel were obtained. A detailed analysis of the effect of velocity and groove size on the drag reduction effect of the groove was also carried out to demonstrate the drag reduction mechanism of the V-shaped groove microstructure and to summarize the variation law of the drag reduction rate of the V-shaped groove. The results show that the resistance reduction rate of the V-shaped groove microstructure decreases with the increase of blood flow velocity, increases with the increase of groove width, and increases and then decreases with the increase of groove depth. The velocity range used in this paper is 0.3–0.6 m/s, the groove width varies from 0 to 0.3 mm, and the groove depth varies from 0 to 0.3 mm.

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Effect of V-Shaped Groove Microstructure on Blood Flow Resistance in Bionic Artificial Blood Vessels

et al. 2023

Applied Bionics and Biomechanics

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On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition

Jenaliyev

Bektemesov

Yergaliyev

2023

Journal of Inverse and Ill-Posed Problems

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The theory of inverse problems is an actively studied area of modern differential equation theory. This paper studies the solvability of the inverse problem for a linearized system of Navier–Stokes equations in a cylindrical domain with a final overdetermination condition. Our approach is to reduce the inverse problem to a direct problem for a loaded equation. In contrast to the well-known works in this field, our approach is to find an equation for a loaded term whose solvability condition provides the solvability of the original inverse problem. At the same time, the classical theory of spectral decomposition of unbounded self-adjoint operators is actively used. Concrete examples demonstrate that the assertions of our theorems naturally develop and complement the known results on inverse problems. Various cases are considered when the known coefficient on the right-hand side of the equation depends only on time or both on time and a spatial variable. Theorems establishing new sufficient conditions for the unique solvability of the inverse problem under consideration are proved.

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Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

Cited by 2 publications

References 12 publications

Effect of V-Shaped Groove Microstructure on Blood Flow Resistance in Bionic Artificial Blood Vessels

Effect of V-Shaped Groove Microstructure on Blood Flow Resistance in Bionic Artificial Blood Vessels

On an inverse problem for a linearized system of Navier–Stokes equations with a final overdetermination condition

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