• 한국전산유체공학회지
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• 제21권1호
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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.

• Korean Journal of Mathematics
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• 제4권2호
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• pp.179-193
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• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.

• 한국항공우주학회지
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• 제36권2호
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• pp.123-130
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• 2008

예조건화 나비어스톡스 방정식의 수렴 특성에 미치는 특성 조건수의 영향을 조사하였다. Choi와 Merkle 예조건화를 적용한 경우와 온도 예조건화를 적용한 경우의 수렴 특성을 분석하였다. 공간차분을 위해 예조건화 Roe의 FDS 기법을 적용하였고, 시간적분을 위해 LU-SGS 기법을 적용하였다. 나비어스톡스 방정식의 수렴 특성은 특성 조건수에 크게 영향을 받으며, 최적의 특성 조건수가 존재하는 것을 보였다. 그리고 점성 유동의 최적 특성 조건수는 비점성 유동에 비해 큰 것으로 나타났다.

• 대한기계학회논문집B
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• 제22권9호
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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.

• 통합자연과학논문집
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• 제6권1호
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• pp.53-56
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• 2013

We are interested in the rate of convergence of solutions of 2D Navier-Stokes equations in a smooth bounded domain as the viscosity tends to zero under Navier friction condition. If the initial velocity is smooth enough($u{\in}W^{2,p}$, p>2), it is known that the rate of convergence is linearly propotional to the viscosity. Here, we consider the rate of convergence for nonsmooth velocity fields when the gradient of the corresponding solution of the Euler equations belongs to certain Orlicz spaces. As a corollary, if the initial vorticity is bounded and small enough, we obtain a sublinear rate of convergence.

• 한국항공우주학회지
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• 제36권6호
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• pp.525-531
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• 2008

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집B
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• pp.597-602
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• 2000

In a MEMS(micro-electro mechanical system), the fluid may slip near the surface of a solid and have a discontinuous temperature profile. A numerical prediction in this slip flow region can provide a reasonable guide for the design and fabrication of micro devices. The compressible Navier-Stokes equation with Maxwell/smoluchowski boundary condition is solved for two simple systems; couette flow and pressure driven flow in a long channel. We found that the couette flow could be regarded as an incompressible system in low speed regions. For the pressure driven flow system, we observed nonlinear distribution of pressure in the long channel and numerical results showed a good agreement with the experimental results.

• 대한수학회보
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• 제50권3호
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• pp.753-760
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• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• 대한수학회지
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• 제49권2호
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• pp.315-324
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• 2012

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$([0; T);$L^2$), T > 0, $2{\leq}p{\leq}+\infty$ satisfy a certain condition. This condition common appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain $\epsilon$ tends to zero.

• 대한화학회지
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• 제40권6호
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• pp.409-414
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• 1996

선형 비평형 열역학의 최소 엔트로피 생성원리를 사용하여 정상 평면충격파 형상에 대한 Navier-Stokes 유체방정식의 적용한계를 연구하였다. 해석적 결과를 얻기 위하여 평형상태에 가까운 하류 위치에서 방정식을 선형화 하였다. 하류 극한의 경계조건을 충족하는 Navier-Stokes 방정식의 해를 충격파 진행속도의 마하수 M=1 근처에서 급수전개하였을 때, 일차항까지는 열역학의 요구조건과 부합하였다.