• Title/Summary/Keyword: Navier-Stokes solution

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THE NAVIER-STOKES EQUATIONS WITH INITIAL VALUES IN BESOV SPACES OF TYPE B-1+3/qq,

  • Farwig, Reinhard;Giga, Yoshikazu;Hsu, Pen-Yuan
    • Journal of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1483-1504
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    • 2017
  • We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.

Analytical Solution for Hypersonic Flow on Blunt Bodies (뭉뚝한 물체 주변에 형성된 극초음속유동해석)

  • Baik Doo Sung
    • Journal of computational fluids engineering
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    • v.8 no.4
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    • pp.1-5
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    • 2003
  • A Thin-layer Wavier-Stokes equations are applied for the hypersonic flow over blunt bodies with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and Van Leer are investigated to predict accurately the heating loads along the surface of the body. A mixed scheme has been presented for the differencing the convective terms and the mixed scheme is found to be less dissipative producing accurate solutions.

Numerical Analysis of Ocean Wave by Multi-Grid Method (복합격자 방법에 의한 해양파의 수치해석)

  • 곽승현
    • Journal of Korean Port Research
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    • v.13 no.1
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    • pp.175-182
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    • 1999
  • The ocean wave is hydrodynamically investigated to get more reliable solution. To improve the computational accuracy more fine grids are used with relatively less computer storage on the free surface. One element of the free surface is discretized into more fine grids because the free-surface waves are much affected by the grid size in the finite difference scheme. Here the multi-grid method is applied to confirm the efficiency for the S103 ship model by solving the Navier-Stokes equation for the turbulent flows. According to the computational result approximately 30% can be improved in the free surface generation, Finally the limiting streamlines show numerical result is similar to the experiment by twin tuft.

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Computational Study on the Characteristics of Nonlinear Wave Caused by Breaking Waves of Two-Dimensional Regular Periodic Wave (2차원 진행규칙파열에서의 쇄파현상에 따른 비선형성 파의 특성에 관한 수치적 연구)

  • 박종천;관전수명
    • Journal of Ocean Engineering and Technology
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    • v.10 no.3
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    • pp.50-61
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    • 1996
  • The breaking phenomenon of regular periodic waves generated by a numerical wave maker is simulated by finite-difference method which can cope with strong interface motions. The air and water flows are simultaneously solved in the time-marching solution procedure for the Navier-Stokes equation. A density-function technique is devised for the implemenation of the interface conditions. The accuracy is examined and applied to the simulation of two-dimensional breaking phenomena of periodic gravity waves.

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The Study of the Electroconductive Liquids Flow in a Conduction Magnetohydrodynamic Pump

  • Naceur, Sonia;Kadid, Fatima Zohra;Abdessemed, Rachid
    • Transactions on Electrical and Electronic Materials
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    • v.17 no.5
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    • pp.252-256
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    • 2016
  • This paper deals the study of a linear MHD pump solution used to eliminate and to avoid the dangers of the mercury appearing through pollution and contamination. The formulation of the magnetohydrodynamic phenomena is derived from Maxwell and Navier-Stokes equations are solved using the finite volume method. Simulation results highlight the performance of the pump such as the electromagnetic force, the velocity, and the pressure, the application of Ansys-Fluent software validation these results.

Sensitivity Analysis for the Navier-Stokes Equations with Two-Equation Turbulence Models

  • 김창성;김종암;노오현
    • 한국전산유체공학회:학술대회논문집
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    • 2000.05a
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    • pp.66-72
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    • 2000
  • Aerodynamic sensitivity analysis is performed for the Navier-Stokes equations coupled with two-equation turbulence models using a discrete adjoint method and a direct differentiation method respectively. Like the mean flow equations, the turbulence model equations are also hand-differentiated to accurately calculate the sensitivity derivatives of flow quantities with respect to design variables in turbulent viscous flows. Both the direct differentiation code and the adjoint variable code adopt the same time integration scheme with the flow solver to efficiently solve the differentiated equations. The sensitivity codes are then compared with the flow solver in terms of solution accuracy, computing time and computer memory requirements. The sensitivity derivatives obtained from the sensitivity codes with different turbulence models are compared with each other. Using two-equation turbulence models, it is observed that a usual assumption of constant turbulent eddy viscosity in adjoint methods may lead to seriously inaccurate results in highly turbulent flows.

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REGULARITY OF WEAK SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

  • Choe, Hi-Jun;Jin, Bum-Ja
    • Journal of the Korean Mathematical Society
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    • v.40 no.6
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    • pp.1031-1050
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    • 2003
  • In this paper, we assume a density with integrability on the space $L^{\infty}$(0, T; $L^{q_{0}}$) for some $q_{0}$ and T > 0. Under the assumption on the density, we obtain a regularity result for the weak solutions to the compressible Navier-Stokes equations. That is, the supremum of the density is finite and the infimum of the density is positive in the domain $T^3$ ${\times}$ (0, T). Moreover, Moser type iteration scheme is developed for $L^{\infty}$ norm estimate for the velocity.

EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM

  • Cho, Yong-Geun;Kim, Hyun-Seok
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.645-681
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    • 2008
  • The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain ${\Omega}{\subset}R^3$. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of ${\Omega}$ or decay at infinity when ${\Omega}$ is unbounded.

A Parametric Study on Inlet Duct Treatment for Improving the Operational Stability of a Centrifugal Compressor (운전안정성 향상을 위한 원심 압축기의 유입부 형상변화에 관한 연구)

  • Seo, Tae-Wan;Heo, Man-Woong;Kim, Kwang-Yong
    • The KSFM Journal of Fluid Machinery
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    • v.19 no.5
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    • pp.12-19
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    • 2016
  • In present study, a parametric study of a centrifugal compressor with inlet treatment has been performed numerically using three-dimensional Reynolds-averaged Navier-Stokes equations. The shear stress transport turbulence model was used for analysis of turbulence. The finite volume method and unstructured grid system were used for the numerical solution. Tested parameters were related to the geometry of the inlet duct. It was found that the application of circumferentially distributed holes in the inlet duct improves operational stability of the compressor compared to that with conventional inlet duct.

A Study on Flow Characteristics of Two-Dimensional Backward-Facing Step by CFD (CFD에 의한 2차원 후향계단에서의 재부착 유동특성에 관한 연구)

  • Choi Y. D.;Lee Y. H.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.11a
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    • pp.127-132
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    • 1998
  • The present study is aimed to investigate flow characteristics of Two dimensional backward-facing step by numerical approach. A convection conservative difference scheme based upon SOLA algorithm is used for the solution of the two-dimensional incompressible Navier-Stokes equations to simulate the laminar, transitional and turbulent flow conditions at which the experimental data can be available for the backward-facing step. The twenty kinds of Reynolds number are used for the calculations. In an effort to demonstrate that the reported solutions are dependent on the mesh refinement, computations are performed on seven different meshes of uniformly increasing refinement. Also to investigate the result of inflow dependence, two kinds of the inflow profile are chosen for the laminar flow. As criterion of benchmarking the result of numerical simulation, reattachment length is used for the selected Reynolds numbers.

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