• Title/Summary/Keyword: Navier-Stokes equations

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DERIVATION OF THE g-NAVIER-STOKES EQUATIONS

  • Roh, Jaiok
    • 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.

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Temperature Preconditioning for Improving Convergence Characteristics in Calculating Low Mach Number Flows, II: Navier-Stokes Equations (저속 유동 계산의 수렴성 개선을 위한 온도예조건화 II: 나비어스톡스 방정식)

  • Lee, Sang-Hyeon
    • 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.

THE GLOBAL ATTRACTOR OF THE 2D G-NAVIER-STOKES EQUATIONS ON SOME UNBOUNDED DOMAINS

  • Kwean, Hyuk-Jin;Roh, Jai-Ok
    • 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.

INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN HETEROGENEOUS MEDIA

  • Pak, Hee Chul
    • 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.

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COMPARISON OF COUPLING METHODS FOR NAVIER-STOKES EQUATIONS AND TURBULENCE MODEL EQUATIONS (Navier-Stokes 방정식과 난류모델 방정식의 연계방법 비교)

  • Lee, Seung-Soo;Ryu, Se-Hyun
    • 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.

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ANALYSIS AND COMPUTATIONS OF OPTIMAL AND FEEDBACK CONTROL PROBLEMS FOR NAVIER-STOKES EQUATIONS

  • Lee, Hyung-Chun
    • 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.

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Numerical Simulation of Overtopping of Cnoidal Waves on a Porous Breakwater Using the Boussinesq Equations: Comparison with Solutions of the Navier-Stokes Equations (Boussinesq 식을 사용하여 Cnoid 파의 투수방파제 월파 해석: Navier-Stokes 식 결과와 비교)

  • Huynh, Thanh Thu;Lee, Changhoon;Ahn, Suk Jin
    • 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.

Critical Reynolds Number for the Occurrence of Nonlinear Flow in a Rough-walled Rock Fracture (암반단열에서 비선형유동이 발생하는 임계 레이놀즈수)

  • Kim, Dahye;Yeo, In Wook
    • 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.

Modification of the Cubic law for a Sinusoidal Aperture using Perturbation Approximation of the Steady-state Navier-Stokes Equations (섭동 이론을 이용한 정상류 Navier-Stokes 방정식의 주기함수 간극에 대한 삼승 법칙의 수정)

  • 이승도
    • 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.