• Title/Summary/Keyword: Navier problem

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OPTIMAL CONTROL PROBLEM OF NAVIER-STOKES EQUATIONS FOR THE DRIVEN CAVITY FLOW

  • Lee, Yong-Hun
    • Journal of applied mathematics & informatics
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    • v.6 no.1
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    • pp.291-301
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    • 1999
  • We study an optimal control problem of the fluid flow governed by the navier-Stokes equations. The control problem is formulated with the flow in the driven cavity. Existence of an optimal solution and first-order optimality condition of the optimal control are derived. We report the numerical results for the finite eleme수 approximations of the optimal solutions.

SENSITIVITY ANALYSIS OF A SHAPE CONTROL PROBLEM FOR THE NAVIER-STOKES EQUATIONS

  • Kim, Hongchul
    • Korean Journal of Mathematics
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    • v.25 no.3
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    • pp.405-435
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    • 2017
  • We deal with a sensitivity analysis of an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By using the material derivative method and adjoint variables for a shape sensitivity analysis, we derive the shape gradient of the design functional for the model problem.

NUMERICAL SOLUTION OF A CONSTRICTED STEPPED CHANNEL PROBLEM USING A FOURTH ORDER METHOD

  • Mancera, Paulo F. de A.;Hunt, Roland
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.3 no.2
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    • pp.51-67
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    • 1999
  • The numerical solution of the Navier-Stokes equations in a constricted stepped channel problem has been obtained using a fourth order numerical method. Transformations are made to have a fine grid near the sharp corner and a long channel downstream. The derivatives in the Navier-Stokes equations are replaced by fourth order central differences which result a 29-point computational stencil. A procedure is used to avoid extra numerical boundary conditions near the solid walls. Results have been obtained for Reynolds numbers up to 1000.

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ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS

  • Quyet, Dao Trong
    • Communications of the Korean Mathematical Society
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    • v.29 no.4
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    • pp.505-518
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    • 2014
  • Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

FINITE ELEMENT APPROXIMATION AND COMPUTATIONS OF BOUNDARY OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES FLOWS THROUGH A CHANNEL WITH STEPS

  • Lee, Hyung-Chun;Lee, Yong-Hun
    • Journal of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.173-192
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    • 1999
  • We study a boundary optimal control problem of the fluid flow governed by the Navier-Stokes equations. the control problem is formulated with the flow through a channel with steps. The first-order optimality condition of the optimal control is derived. Finite element approximations of the solutions of the optimality system are defined and optimal error estimates are derived. finally, we present some numerical results.

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PULLBACK ATTRACTORS FOR 2D g-NAVIER-STOKES EQUATIONS WITH INFINITE DELAYS

  • Quyet, Dao Trong
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.519-532
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    • 2016
  • We consider the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations with infinite delays. We prove the existence of a pullback $\mathcal{D}$-attractor for the continuous process associated to the problem with respect to a large class of non-autonomous forcing terms.

PENALIZED APPROACH AND ANALYSIS OF AN OPTIMAL SHAPE CONTROL PROBLEM FOR THE STATIONARY NAVIER-STOKES EQUATIONS

  • Kim, Hong-Chul
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.1-23
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    • 2001
  • This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.

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CONVERGENCE OF THE NEWTON'S METHOD FOR AN OPTIMAL CONTROL PROBLEMS FOR NAVIER-STOKES EQUATIONS

  • Choi, Young-Mi;Kim, Sang-Dong;Lee, Hyung-Chun
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.1079-1092
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    • 2011
  • We consider the Newton's method for an direct solver of the optimal control problems of the Navier-Stokes equations. We show that the finite element solutions of the optimal control problem for Stoke equations may be chosen as the initial guess for the quadratic convergence of Newton's algorithm applied to the optimal control problem for the Navier-Stokes equations provided there are sufficiently small mesh size h and the moderate Reynold's number.

EXISTENCE AND LONG-TIME BEHAVIOR OF SOLUTIONS TO NAVIER-STOKES-VOIGT EQUATIONS WITH INFINITE DELAY

  • Anh, Cung The;Thanh, Dang Thi Phuong
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.379-403
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    • 2018
  • In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.