• 한국전산구조공학회논문집
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• 제15권4호
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• pp.675-691
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• 2002

본 연구의 목적은 Navier-Stokes 유체와 같은 대용량 문제를 위한 최적화 기법의 개발에 있다. 이를 위해 본 연구에서는 reduced Hessian sequential quadratic programming을 개발하였다. 첫째, 유체의 해석을 위한 평형 방정식을 최적화 과정에서 제거하여 변수를 줄였고, 또한 평형방정식과 최적화 과정에서 연속기법을 사용하여 최적해를 보장하면서 더욱 해에 쉽게 접근하도록 하였다. 그리고 각 단계에서는 테일러 시리즈를 이용한 근사치를 이용하여 각 단계에서 대단히 좋은 초기치 값을 제공하여 최적해에 더욱 빠르게 접근하게 하고 아울러 유체의 평형방정식을 풀 때에도 해에 더욱 빠르고 쉽게 접근하도록 하였다. 이 기법을 항력을 줄이기 위한 유체의 최적 제어를 위한 문제에 적용하였다. 유체의 흐름을 제어하기 위하여 물체의 경계면에서 유체의 흡입(suction)과 방축(injection)이라는 기법을 사용하여 경계면에서 속도를 제어하였고, 목적함수로써 항력을 표현하기 위하여 에너지 소실의 변화율을 사용하였다. 예제를 통해 본 연구에서 개발한 최적화 기법의 효용성을 입증하였다.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.645-658
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• 2014

Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.

• 한국컴퓨터그래픽스학회논문지
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• 제14권4호
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• pp.1-5
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• 2008

본 논문은 유체 시뮬레이션의 격자 내 상세도를 와류입자법(Vortex Particle Method)를 사용하여 향상시킬 수 있는 새로운 방법을 제안한다. 비압축 Navier-Stokes 방정식을 풀어 낸 속도장(Velocity Field)으로 유체의 거시적인 움직임을, 와류입자법으로 생성한 와도장(Vorticity Field)으로 유체의 미세한 움직임을 표현한다. 이 기법은 고해상도 격자에서 선형시스템을 풀지 않기 때문에 고해상도 유체 시뮬레이션을 효율적으로 할 수 있고, 강한 난류 효과를 만들어 낼 수 있다.

• 대한수학회보
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• 제61권3호
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• pp.637-669
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• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1999년도 제29회 춘계학술대회
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• pp.127-132
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• 1999

The inlet pressure build-up at the leading edge of bearings which have discontinuous lubrication surface is analyzed theoretically. The analyses of Inlet pressure build-up is obtained by means of full Navier-stokes equations. Beam-warming method is used to solve navier-stokes equations. The results show that inlet pressure is above atmosphere pressure in front of leading edge of hearing.

• 대한수학회지
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• 제34권4호
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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.

• 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.

• 대한수학회보
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• 제46권4호
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• pp.627-644
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• 2009

The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method to prove optimal accuracy via energy estimate. The main key in this proof is to construct the intermediate equation which is formed to gauge-Uzawa algorithm. We will estimate velocity errors via comparing with the intermediate equation and then evaluate pressure errors via subtracting gauge-Uzawa algorithm from Navier-Stokes equations.

• International Journal of Aeronautical and Space Sciences
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• 제10권2호
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• pp.125-133
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• 2009

To numerically simulate aerodynamics of rotor-airframe interaction in a rigorous manner, we need to solve the Navier-Stokes system for a rotor-airframe combination as a whole. This often imposes a serious computational burden since rotating blades and a stationary body have to be simultaneously dealt with. An efficient alternative is to adopt a momentum source method in which the action of rotor is approximated as momentum source over a rotor disc plane in a stationary computational domain. This makes the simulation much simpler. For unsteady simulation, the instantaneous momentum sources are assigned only to a portion of disk plane corresponding to blade passage. The momentum source is obtained by using blade element theory with dynamic inflow model. Computations are carried out for the simple rotor-airframe model (the Georgia Tech model) and the results of the simulation are compared with those of the full Navier-Stokes simulation with moving mesh system for rotor and with experimental data. It is shown that the present simulation yields results as good as those of the full Navier-Stokes simulation.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.2157-2161
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• 2003

In this paper, the response surface method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan, is described. For numerical analysis, Reynolds-averaged Navier-Stokes equations with standard k-e turbulence model are transformed into non-orthogonal curvilinear coordinate system, and are discretized with finite volume approximations. Due to the large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models for economic calculations. Linear Upwind Differencing Scheme(LUDS) is used to approximate the convection terms in the governing equations. SIMPLEC algorithm is used as a velocity-pressure correction procedure. Design variables, location of cur off, radius of cut off, expansion angle of scroll and width of impeller were selected to optimize the shapes of scroll and blades. Data points for response evaluations were selected by D-optimal design, and linear programming method was used for the optimization on the response surface. As a main result of the optimization, the efficiency was successfully improved. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time