• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.151-164
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• 2001

In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate values of pressure are obtained by a finite difference scheme.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.359-373
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• 2012

The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.363-376
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• 2002

Stability result is obtained for the approximation of the stationary Stokes problem with nonconforming elements proposed by Douglas et al [1] for the velocity and discontinuous piecewise constants for the pressure on qudrilateral elements. Optimal order $H^1$and $L^2$error estimates are derived.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.25-40
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• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.

• 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.

• 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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.1000-1002
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• 2017

Here, the unsteady Navier-Stokes solver has been developed using implicit dual time stepping method. The implicit dual time stepping method introduced the pseudo time step for solving the new residual including the steady state residual and real time derivative. For the validation of code, Stokes 2nd problem, the laminar flow on the oscillating flat plate was selected and compare the calculating results with analytic solutions. The calculating velocity profile and skin friction has a good agreement with analytic solutions.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.733-763
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• 2006

We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1239-1266
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• 2020

In this paper, some novel discrete formulations for stabilizing the mixed finite element method Q1-Q0 (bilinear velocity and constant pressure approximations) are introduced and discussed for the generalized Stokes problem. These are based on stabilizing discontinuous pressure approximations via local jump operators. The developing idea consists in a reduction of terms in the local jump formulation, introduced earlier, in such a way that stability and convergence properties are preserved. The computer implementation aspects and numerical evaluation of these stabilized discrete formulations are also considered. For illustrating the numerical performance of the proposed approaches and comparing the three versions of the local jump methods alongside with the global jump setting, some obtained results for two test generalized Stokes problems are presented. Numerical tests confirm the stability and accuracy characteristics of the resulting approximations.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1079-1101
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• 2020

This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a levelset curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.