• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.213-218
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• 2006

The 2D g-Navier-Stokes equations are a certain modified Navier-Stokes equations and have the following form, $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla})u+{\nabla}p=f$$, in ${\Omega}$ with the continuity equation ${\nabla}{\cdot}(gu)=0$, in ${\Omega}$, where g is a suitable smooth real valued function. In this paper, we will derive 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In addition, we will see the relationship between two equations.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.12
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• pp.1075-1081
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• 2007

The temperature preconditioning is applied to the Navier-Stokes equations. Also, a new concept of diffusion Mach numbers is introduced to modify the reference Mach number for the Navier-Stokes equations. Flows over a circular cylinder were calculated at different Reynolds numbers. It is shown that the temperature preconditioning improves the convergence characteristics of Navier-Stokes equations. Also, it is shown that the modified reference Mach number alleviates the convergence problems at locally low speed regions.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.731-749
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• 2005

In this paper, we study the two dimensional g-Navier­Stokes equations on some unbounded domain ${\Omega}\;{\subset}\;R^2$. We prove the existence of the global attractor for the two dimensional g-Navier­Stokes equations under suitable conditions. Also, we estimate the dimension of the global attractor. For this purpose, we exploit the concept of asymptotic compactness used by Rosa for the usual Navier-Stokes equations.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.555-561
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• 2019

In this paper we consider degenerate compressible Navier-Stokes equations giving rise to a variety of mathematical problems in many areas. We study the long time behavior for the degenerate compressible Navier-Stokes equations with damping.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.335-347
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• 2006

The homogenization of non-stationary Navier-Stokes equations on anisotropic heterogeneous media is investigated. The effective coefficients of the homogenized equations are found. It is pointed out that the resulting homogenized limit systems are of the same form of non-stationary Navier-Stokes equations with suitable coefficients. Also, steady Stokes equations as cell problems are identified. A compactness theorem is proved in order to deal with time dependent homogenization problems.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.111-116
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• 2005

Two coupling methods for the Navier-Stokes equations and a two-equation turbulence model equations are compared. They are the strongly coupled method and the loosely coupled method. The strongly coupled method solves the Navier-Stokes equations and the two-equation turbulence model equations simultaneously, while the loosely coupled method solves the Navier-Stokes equation with the turbulence viscosity fixed and subsequently solves the turbulence model equations with all the flow quantities fixed. In this paper, performances of two coupling methods are compared for two and three-dimensional problems.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.841-857
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• 1997

We present analysis and some computational methods for boundary optimal and feedback control problems for Navier-Stokes equations. We use one example to illustrate our methodology and ideas which are applicable to general control problems for Navier-Stokes equations. First, we discuss the existence of optimal solutions and derive an optimality system of equations from which an optimal solution may be computed. Then we present a gradient type iterative method. Finally, we present some numerical results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.2
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• pp.41-49
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• 2019

We approximately obtain heights of cnoidal waves overtopping on a porous breakwater using both the one-layer Boussinesq equations (Vu et al., 2018) and the two-layer Boussinesq equations (Huynh et al., 2017). For cnoidal waves overtopping on a porous breakwater, we find through numerical experiments that the heights of cnoidal waves overtopping on a low-crested breakwater (obtained by the Navier-Stokes equations) are smaller than the heights of waves passing through a high-crested breakwater (obtained by the one-layer Boussinesq equations) and larger than the heights of waves passing through a submerged breakwater (obtained by the two-layer Boussinesq equations). As the cnoidal wave nonlinearity becomes smaller or the porous breakwater width becomes narrower, the heights of transmitting waves obtained by the one-layer and two-layer Boussinesq equations become closer to the height of overtopping waves obtained by the Navier-Stokes equations.

• Economic and Environmental Geology
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• v.52 no.4
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• pp.291-297
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• 2019

Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.

• Tunnel and Underground Space
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• v.13 no.5
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• pp.389-396
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• 2003

It is shown that the cubic law can be modified regarding the steady-state Navier-Stokes equations by using perturbation approximation method for a sinusoidal aperture variation. In order to adopt the perturbation theory, the sinusoidal function needs to be non-dimensionalized for the amplitude and wavelength. Then, the steady-state Navier-Stokes equations can be solved by expanding the non-dimensionalized stream function with respect to the small value of the parameter (the ratio of the mean aperture to the wavelength), together with the continuity equation. From the approximate solution of the Navier-Stokes equations, the basic cubic law is successfully modified for the steady-state condition and a sinusoidal aperture variation. A finite difference method is adopted to calculate the pressure within a fracture model, and the results of numerical experiments show the accuracy and applicability of the modified cubic law. As a result, it is noted that the modified cubic law, suggested in this study, will be used for the analysis of fluid flow through aperture geometry of sinusoidal distributions.