• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1950-1960
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• 2006

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes' waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes' waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes' waves' interaction. The proposed method has a very fast convergence rate.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.283-289
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• 2006

Roh[1] derived 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In this paper, we will see the space $L^2({\Omega},\;g)$, which is the weighted space of $L^2({\Omega})$, as natural generalized space of $L^2({\Omega})$ which is mathematical setting for Navier-Stokes equations. Our future purpose is to use the space $L^2({\Omega},\;g)$ as mathematical setting for the g-Navier-Stokes equations. In addition, we will see Helmoltz-Leray projection on $L^2_{per}({\Omega},\;g)$) and compare with the one on $L^2_{per}({\Omega})$.

• 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.

• 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 Society for Aeronautical & Space Sciences
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• v.32 no.8
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• pp.1-11
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• 2004

A comprehensive study has been made for the investigation of the convergence and stability characteristics of the LU scheme for solving the Navier-Stokes equations on unstructured meshes. For this purpose the characteristics of the LU scheme was initially studied for a scalar model equation. Then the analysis was extended to the Navier-Stokes equations. It was shown that the LU scheme has an inherent stiffness in the streamwise direction. This stiffness increases when the grid aspect ratio becomes high and the cell Reynolds number becomes small. It was also shown that the stiffness related to the grid aspect ratio can be effectively eliminated by performing proper subiteration. The results were validated for a flat-plate turbulent flow.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

• The Journal of Internal Korean Medicine
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• v.38 no.4
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• pp.409-418
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• 2017

In Korea, Rhus verniciflua Stokes is used to purge hardness, alleviate blood stasis, and treat cancer. However, the mechanisms of related anti-cancer activity are not fully understood in human cancer cells. This study investigated the anti-cancer effects and mechanisms of Rhus verniciflua Stokes on MDA-MB-231 human breast cancer cells and found that treatment with a Rhus verniciflua Stokes extract resulted in time- and concentration-responses that indicated growth inhibition of breast cancer cells by induced apoptosis. This was followed by a decrease in mitochondrial membrane potential; the activation of caspase-3, -8, and -9; and the up-regulation of tBid. Caspase-dependent apoptosis was induced through the inhibition of phosphatidylinositol 3-kinase (PI3K) and the Akt signaling pathway. This study provides evidence that Rhus verniciflua Stokes might be useful for the treatment of breast cancer.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.753-765
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• 2003

A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.

• 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.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.187-200
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• 1992

A general scheme is developed to determine the Langrangian motions of water particles by the Eulerian velocity at their mean positions by using Taylor's theorem. Utilizing the Stokes finite-amplitude wave theory, the orbital motions and the mass transport velocity including the effects of higher-order wave components are determined. The fifth-order approximation of orbital motion gives very good predictions of actual water particle motion in Stokes fifth-order wave theory except near the free-surface. The fifth-order theory predicts the mass transport velocity less than that given by the existing second-order theory over the whole water depth.