• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.9
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• pp.1325-1334
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• 1998

The objectives of the present study are to develop a systematic method rather than a conventional trial-and-error method for an optimal shape design using a mathematical theory, and to apply it to engineering problems. In the present study, an optimal condition for a minimum pressure loss in a two-dimensional curved duct flow is derived and then an optimal shape of the curved duct is designed from the optimal condition. In the design procedure, one needs to solve the adjoint Navier-Stokes equations which are derived from the Navier-Stokes equations and the cost function. Therefore, a computer code of solving both the Navier-Stokes and adjoint Navier-Stokes equations together with an automatic grid generation is developed. In a curved duct flow, flow separation occurs due to an adverse pressure gradient, resulting in an additional pressure loss. Optimal shapes of a curved duct are obtained at three different Reynolds numbers of 100, 300 and 800, respectively. In the optimally shaped curved ducts, the separation region does not exist or is significantly reduced, and thus the pressure loss along the curved duct is significantly reduced.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.637-669
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• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1129-1137
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• 1996

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.599-605
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• 2003

For practical calculations, the Reynolds equation is frequently used to analyze the lubricating flow. The full Navier-Stokes Equations are used to find validity limits of Reynolds equation in a lubricating flow regime by result comparison. As the amplitude of wavy upper wall increased at a given average channel height, the difference between Navier-Stokes and lubrication theory decreased slightly : however, as the minimum distance in channel throat increased, the differences in the maximum pressure between Navier-Stokes and lubrication theory became large.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.123-130
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Navier-Stokes equations were investigated. The two-dimensional preconditioned Navier-Stokes adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Navier-Stokes equations are strongly affected by the characteristic condition number. Also it is shown that the optimal characteristic condition numbers for viscous flows are larger than that in inviscid flows.

• Journal of Korea Water Resources Association
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• v.45 no.6
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• pp.545-555
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• 2012

A numerical modeling has become increasingly popular and more important to the study of water waves with a rapid advancement of computer technology. However, different types of problems are induced during simulating wave motion. One of the key problems is re-reflection to a computation domain at the incident boundary. The internal wave generating-absorbing boundary conditions have been commonly used in numerical wave models to prevent re-reflection. For the Navier-Stokes equations model, the internal wave maker using a mass source function of the continuity equation has been used to generate various types of waves. Nonetheless, almost every numerical experiment is performed in two dimensions and only a few tests have been expanded to three dimensions. More recently, a momentum source function of the Boussinesq equations is applied to generate essentially directional waves in the three dimensional Navier-Stokes equations model. In this study, the internal wave maker using a momentum source function is employed to generate targeted linear waves in the three-dimensional LES model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.313-324
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• 1992

Two-dimensional Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system, then mapped into a generalized body-fitted coordinate system. All direction of viscous terms are incorporated and turbulent effects are modeled using the Baldwin-Lomax algebraic model. Equation are discretized using finite difference method on the C-type grids and solved using implicit LU-ADI decomposition scheme. Calculations are made at a VKI turbine cascade flow in a transonic wind-tunnel and compared to experimental data. Present numerical scheme is shown to be in good agreement with the previous experimental results and simulates the two-dimensional viscous flow phenomena.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.96-101
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• 1998

Various discretiation methods of Laplacian operator in the Pressure-Poisson equation are investigated for the solution of incompressible Navier-Stokes equations using the non-staggered grid. Laplacian operators previously proposed by other researchers are applied to a Driven-Cavity problem. The computational results are compared with those of Ghia. The results show the characteristics of the discrete Laplacian operators.

• 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.