A BOUNDARY CONTROL PROBLEM FOR VORTICITY MINIMIZATION IN TIME-DEPENDENT 2D NAVIER-STOKES EQUATIONS

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Download Full-text

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽

10.1515/anly-2019-0049 ◽

2020 ◽

Vol 40 (3) ◽

pp. 127-150

Author(s):

Tania Biswas ◽

Sheetal Dharmatti ◽

Manil T. Mohan

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Stokes Equations ◽

Minimum Principle ◽

Immiscible Fluids ◽

Second Order ◽

Navier Stokes ◽

Distributed Optimal Control ◽

Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

Download Full-text

A posteriori error estimates of finite element method for the time-dependent Navier–Stokes equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2017.07.005 ◽

2017 ◽

Vol 315 ◽

pp. 13-26 ◽

Cited By ~ 1

Author(s):

Tong Zhang ◽

ShiShun Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Stokes Equations ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Time Dependent ◽

Navier Stokes ◽

A Posteriori ◽

Navier Stokes Equations ◽

A Posteriori Error

Download Full-text

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

Journal of Fluid Mechanics ◽

10.1017/s0022112076002486 ◽

1976 ◽

Vol 78 (2) ◽

pp. 355-383 ◽

Cited By ~ 177

Author(s):

H. Fasel

Keyword(s):

Finite Difference ◽

Stability Theory ◽

Stokes Equations ◽

Time Dependent ◽

Linear Stability Theory ◽

Navier Stokes ◽

Experimental Measurements ◽

Navier Stokes Equations ◽

The Stability ◽

Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Download Full-text