• Title/Summary/Keyword: Stokes problem

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Fourier Approximation of Nonlinear Standing Waves (비선형 정상파의 Fourier급수 해석)

  • 전인식;안희도
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.4 no.4
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    • pp.219-224
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    • 1992
  • A numerical method using the truncated Fourier series is presented to predict the wave potential and water surface profile for two dimensional nonlinear standing waves. The unknown coefficients of the series are to be determined through the Newton solution of nonlinear simultaneous equations given by the governing equation and boundary conditions of the problem. In order to prove the effectiveness of the present method. an existing Stokes-like perturbation method is considered together, and a hydraulic experiment for measuring water surface profile and wave pressure is performed as well. The results are such that the present method can generally give exact solutions even for relatively big wave stiffness regardless of the water depth condition. It also demonstrates its validity by showing double humps in the crest of temporal wave pressure profile which normally appear in strongly nonlinear standing waves.

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A Study on the Numerical Simulation Method of Two-dimensional Incompressible Fluid Flows using ISPH Method (ISPH법을 이용한 2차원 비압축성 유체 유동의 수치시뮬레이션 기법 연구)

  • Kim, Cheol-Ho;Lee, Young-Gill;Jeong, Kwang-Leol
    • Journal of the Society of Naval Architects of Korea
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    • v.48 no.6
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    • pp.560-568
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    • 2011
  • In SPH(Smoothed Particle Hydrodynamics) method, the fluid has been assumed that it is weakly compressible to solve the basic equations composed of Navier-Stokes equations and continuity equation. That leads to some drawbacks such as non-physical pressure fluctuations and a restriction as like small time steps in computation. In this study, to improve these problems we assume that the fluid is incompressible and the velocity-pressure coupling problem is solved by a projection method(that is, by ISPH method). The two-dimensional computation results of dam breaking and gravitational wave generation are respectively compared with the results of finite volume method and analytical method to confirm the accuracy of the present numerical computation technique. And, the agreements are comparatively acceptable. Subsequently, the green water simulations of a two-dimensional fixed barge are carried out to inspect the possibility of practical application to ship hydrodynamics, those correspond to one of the violent free surface motions with impact loads. The agreement between the experimental data and the present computational results is also comparatively good.

A Study on Ludo-narrative Harmony in the Video Game "Ghost of Tsushima" (비디오 게임 "고스트 오브 쓰시마"의 게임플레이-스토리의 조화성 고찰)

  • Chun, Bumsue
    • Journal of Korea Game Society
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    • v.21 no.5
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    • pp.87-104
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    • 2021
  • Ludo-narrative dissonance is a prevalent problem among open-world genre video games. However, Ghost of Tsushima (2020) alleviates this issue by designing its characters and narrative structure influenced by Akira Kurosawa's samurai films. The game's protagonist represents "Bushido," a samurai code, and the structure exudes similarity to Joseph Campbell's "Hero's Journey," which heavily influenced Kurosawa's films. The developers also designed the gameplay mechanics such as level-up system, map design, and side quests based on these narrative traits, ultimately making the goal of the narrative and the gameplay mechanics cohesive.

Forced vibration of the hydro-elastic system consisting of the orthotropic plate, compressible viscous fluid and rigid wall

  • Akbarov, Surkay D.;Huseynova, Tarana V.
    • Coupled systems mechanics
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    • v.8 no.3
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    • pp.199-218
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    • 2019
  • This paper studies the forced vibration of the hydro-elastic system consisting of the anisotropic (orthotropic) plate, compressible viscous fluid and rigid wall within the scope of the exact equations and relations of elastodynamics for anisotropic bodies for describing of the plate motion, and with utilizing the linearized exact Navier-Stokes equations for describing of the fluid flow. For solution of the corresponding boundary value problem it is employed time-harmonic presentation of the sought values with respect to time and the Fourier transform with respect to the space coordinate on the coordinate axis directed along the plate length. Numerical results on the pressure acting on the interface plane between the plate and fluid are presented and discussed. The main aim in this discussion is focused on the study of the influence of the plate material anisotropy on the frequency response of the mentioned pressure. In particular, it is established that under fixed values of the shear modulus of the plate material a decrease in the values of the modulus of elasticity of the plate material in the direction of plate length causes to increase of the absolute values of the interface pressure. The numerical results are presented not only for the viscous fluid case but also for the inviscid fluid case.

On the dispersion of waves propagating in "plate+fluid layer" systems

  • Akbarov, Surkay D.;Negin, Masoud
    • Coupled systems mechanics
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    • v.10 no.2
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    • pp.123-142
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    • 2021
  • The paper deals with the study of the dispersion of quasi-Lamb waves in a hydro-elastic system consisting of an elastic plate, barotropic compressible inviscid fluid, and rigid wall. The motion of the plate is described using the exact equations of elastodynamics, however, the flow of the fluid using the linearized equations and relations of the Navier-Stokes equations. The corresponding dispersion equation is obtained and this equation is solved numerically, as a result of which the corresponding dispersion curves are constructed. The main attention is focused on the effect of the presence of the fluid and the effect of the fluid layer thickness (i.e., the fluid depth) on the dispersion curves. The influence of the problem parameters on the dispersion curves related to the quasi-Scholte wave is also considered. As a result of the analyses of the numerical results, concrete conclusions are made about the influence of the fluid depth, the rigid wall restriction on the fluid motion, and the material properties of the constituents on the dispersion curves. During the analyses, the zeroth and the first four modes of the propagating waves are considered.

The Effect of Slip on the Convective Instability Characteristics of the Stagnation Point Flow Over a Rough Rotating Disk

  • Mukherjee, Dip;Sahoo, Bikash
    • Kyungpook Mathematical Journal
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    • v.61 no.4
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    • pp.831-843
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    • 2021
  • In this paper we look at the three dimensional stagnation point flow problem over a rough rotating disk. We study the theoretical behaviour of the stagnation point flow, or forced flow, in the presence of a slip factor in which convective instability stationary modes appear. We make a numerical investigation of the effects of slip on the behaviour of the flow components of the stagnation point flow where the disk is rough. We provide, for the first time in the literature, a complete convective instability analysis and an energy analysis. Suitable similarity transformations are used to reduce the Navier-Stokes equations and the continuity equation into a system of highly non-linear coupled ordinary differential equations, and these are solved numerically subject to suitable boundary conditions using the bvp4c function of MATLAB. The convective instability analysis and the energy analysis are performed using the Chebyshev spectral method in order to obtain the neutral curves and the energy bars. We observe that the roughness of the disk has a destabilising effect on both Type-I and Type-II instability modes. The results obtained will be prominently treated as benchmarks for our future studies on stagnation flow.

Attenuation of quasi-Lamb waves in a hydroelastic system "elastic plate+compressible viscous fluid+rigid wall"

  • Akbarov, Surkay D.;Negin, Mesut
    • Structural Engineering and Mechanics
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    • v.81 no.4
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    • pp.443-459
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    • 2022
  • The paper studies the dispersion and attenuation of propagating waves in the "plate+compressible viscous fluid layer" system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.

A STUDY ON THE FLOW CHARACTERISTICS OF AIR-KNIFE USING A CONSTANT EXPANSION RATE NOZZLE (팽창률이 일정한 노즐을 사용한 AIR-KNIFE 유동에 관한 연구)

  • Lee, Dong-Won;Kang, Nam-Cheol;Kim, Guen-Young;Kwon, Young-Doo;Kwon, Soon-Bum
    • Journal of computational fluids engineering
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    • v.13 no.4
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    • pp.1-7
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    • 2008
  • In the process of continuous hot-dip galvanizing, it is well known that the gas wiping through an air knife system is most effective because of its uniformity in coating thickness, possibility of thin coating, workability in high speed, and simplicity of control. However, gas wiping used in the galvanizing process brings about a problem of splashing at the strip edge above a certain high speed of process. It is also known that the problem of edge splashing is more harmful than that at the mid strip surface. For a given liquid(of a certain viscosity and surface tension), the onset of splashing mainly depends upon the strip velocity, the gas-jet pressure, and the nozzle's stand-off distance. In these connections in the present study, we proposed three kinds of air knife system having nozzles of constant expansion rate, and compared the jet structures issuing from newly proposed nozzle systems with the result by a conventional one. In numerical analysis, the governing equations are consisted of two-dimensional time dependent Navier-Stokes equations, and the standard k-${\varepsilon}$ turbulence model is employed to solve turbulence stress and so on. As the result, it is found that we had better use the constant expansion-rate nozzle which can be interpreted from the point view of the energy saving for the same coating thickness. Also, we better reduce the size of separation bubble and enhance the cutting ability at the strip surface, by using an air-knife having constant expansion-rate nozzle.

A Numerical Analysis on the Coating Thickness in Continuous Hot-Dip Galvanizing (연속 아연 도금 코-팅 두께에 관한 수치 해석적 연구)

  • Lee, Dong-Won;Shin, Seung-Young;Kim, Byung-Ji;Kwon, Young-Doo;Kwon, Soon-Bum
    • Proceedings of the KSME Conference
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    • 2007.05b
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    • pp.2955-2960
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    • 2007
  • To control the coating thickness of zinc in the process of continuous hot-dip galvanizing, it is known from early day that the gas wiping through an air knife system is the most effective because of the obtainable of uniformity of coating thickness, possibility of thin coating, working ability in high speed and simplicity of control. But, the gas wiping using in the galvanizing process brings about a problem of splashing from the strip edge for a certain high speed of coating. And, it is known that the problem of splashing is caused mainly by the existence of separation bubble at the neighbor of the strip surface. In theses connections, in the present study, we proposed two kinds of air knife systems having the same expansion rate of nozzle, and the jet structures and coating thicknesses from a conventional and new proposed nozzles are compared. In numerical analysis, the governing equations consisted of two-dimensional time dependent Navier-Stokes equations, standard ${\kappa}-{\varepsilon}$ turbulence model to solve turbulence stress and so on are employed. As a result, it is found that it had better to use the constant rate nozzle from the point view of the energy saving to obtain the same coating thickness. Also, to reduce the size of separation bubble and to enhance the cutting ability at the strip, it is recommendable to use an air knife having the constant expansion rate nozzle.

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On the Vorticity and Pressure Boundary Conditions for Viscous Incompressible Flows (비압축성 점성유동의 와도와 압력 경계조건)

  • Suh J.-C.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.05a
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    • pp.15-28
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    • 1998
  • As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.

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