• 대한기계학회논문집B
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• 제23권2호
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• pp.198-209
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• 1999

This study reports the selection of dependent variables for momentum equations in general curvilinear coordinates. Catesian, covariant and contravariant velocity components were examined for the dependent variable. The focus of present study is confined to staggered grid system Each dependent variable selected for momentum equations are tested for several flow fields. Results show that the selection of Cartesian and covariant velocity components intrinsically can not satisfy mass conservation of control volume unless additional converting processes ore used. Also, Cartesian component can only be used for the flow field in which main-flow direction does not change significantly. Convergence rate for the selection of covariant velocity component decreases quickly as with the increase of non-orthogonality of grid system. But the selection of contravariant velocity component reduces the total mass residual of discretized equations rapidly to the limit of machine accuracy and the solutions are insensitive to the main-flow direction.

• International Journal of Aeronautical and Space Sciences
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• 제7권2호
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• pp.155-174
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• 2006

Parabolized stability equations for compressible flows in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Compressible and incompressible flat plate flow stability under two-dimensional and three¬dimensional disturbances has been investigated to test the present code. Results of the present computation are found to be in good agreement with the multiple scale analysis and DNS data. Stability calculation results by the present PSE code for compressible boundary layer at Mach numbers ranging from 0.02 to 1.5 are also presented and are again seen to be as accurate as the spectral method.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 추계 학술대회논문집
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• pp.134-140
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• 2007

Nonlinear parabolized stability equations for compressible flow in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Blasius flow is tested. The results of the present computation show good agreement with DNS data. Nonlinear interaction can make the T-S fundamental wave more unstable and the onset of its amplitude decay is shifted downstream relative to linear case. For nonlinear calculations, rather small difference in initial amplitude can produce large change during nonlinear region. Compressible secondary instability at Mach number 1.6 is also simulated and showed that 1.1% initial amplitude for primary mode is enough to trigger the secondary growth.

• 대한기계학회논문집B
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• 제25권11호
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• pp.1500-1508
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• 2001

This paper represents the importance of dependent variables in non-orthogonal curvilinear coordinates just as the importance of those variables of convective scheme and turbulence model in computational fluid dynamics. Each of Cartesian, physical covariant and physical contravariant velocity components was tested as the dependent variables of momentum equations in the staggered grid system. In the flow past a circular cylinder, the results were computed to use each of three variables and compared to experimental data. In the skewed driven cavity flow, the results were computed to check the grid dependency of the variables. The results used in Cartesian and physical contravariant components of velocity in cylinder flow show the nearly same accuracy. In the case of Cartesian and contravariant component, the same number of vortex was predicted in the skewed driven cavity flow. Vortex strength of Cartesian component case has about 30% lower value than that of the other two cases.

• Journal of Advanced Marine Engineering and Technology
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• 제18권3호
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• pp.94-101
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• 1994

To develope the new simulator for the analysis of fluid flow information, the influence of various convective difference schemes were evaluated. General curvilinear coordinate system with nonorthogonal grids was adopted for the successful analysis of various complex geometries. Computation results show that if we can not obtain full grid numbers within available computational environment, we need to use higher order finite difference schemes to keep the prediction accuracy.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 추계학술발표대회 논문집
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• pp.173-176
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• 2000

Finite element model based on the Naghdi's shell theory in the general tensor-based form is formulated in the present study. Partial mixed variational functional for assumed strain is formulated in order to avoid the severe locking troubles known as transverse shear and membrane locking. The proposed assumed strain element in general tensor Naghdi's shell model provides very accurate solutions for thin shells in benchmark problems. In additions, linear elastic constitutive equations are given in the general curvilinear coordinate system including anisotropic layered structures. Thus laminated composited shell structures are easily analyzed in the present formulation.

• Advanced Composite Materials
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• 제18권1호
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• pp.21-42
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• 2009

The vibration characteristics of post-buckled laminated composite doubly curved shells are investigated. The finite element method is used for the analysis of post-buckling and free vibration of post-buckled laminated shells. The geometric non-linear finite element model includes the general non-linear terms in the strain-displacement relationships. The shell geometry used in the present formulation is derived using an orthogonal curvilinear coordinate system. Based on the principle of virtual work the non-linear finite element equations are derived. Arc-length method is implemented to capture the load-displacement equilibrium curve. The vibration characteristics of post-buckled shell are performed using tangent stiffness obtained from the converged deflection. The code is first validated and then employed to generate numerical results. Parametric studies are performed to analyze the snapping and vibration characteristics. The relationship between loads and fundamental frequencies and between loads and the corresponding displacements are determined for various parameters such as thickness ratio and shallowness.

• 한국해안해양공학회지
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• 제1권1호
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• pp.22-30
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• 1989

파랑은 천해역을 진행하면서 천수효과에 의한 굴절 및 구조물에 의한 회절, 흐름의 영향, 반사등에 의한 변형을 일으킨다. 굴절 및 회절에 의한 파랑변형을 예측하기 위하여 흐름이 고려된 비정상 상태의 Kirby(1986a)의 식을 이용하여 회절이 고려된 기초방정식을 유도하고, 좌표계를 파향선식에 의한 직교곡선 좌표계로 변환한 후 양해법으로 반복계산을 행하여 해를 구하는 수치 모형을 개발하였다. 수치 모형의 적용성을 검토하기 위하여 다음과 같은 조건에서 계산하였으며, 기존의 계산결과 및 실험결과와 비교 검토하였다. 1) 일정 수심상에서 원형 천퇴 주변의 파랑변형 2) 사면상에서 타원형 천퇴 주변의 파랑변형 3) 사면상에서 파랑이 입사각을 갖고 입사할 경우 구조물 주변의 파랑변형 본 모형의 수치해를 검토한 결과 기존의 연구결과와 잘 일치하였다.

• 한국해안해양공학회지
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• 제17권3호
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• pp.158-165
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• 2005

Level Set방법을 사용하여 액체와 기체의 서로 다른 상을 함께 해석하는 연구를 수행하였다. Level Set함수는 상의 경계면에서부터 부호를 갖는 거리함수로 정의되며,계산 격자에서 함수 값의 부호에 따라 각 상을 구분하고 물성치를 부여한다. 본 논문에서는 비압축성 유체의 보존식에 Level Set함수의 이동식을 연계하여 이상유동을 모사하는 지배방정식을 구성하였으며, 이를 pseudo-compressibility 방법으로 함께 풀었다. 이 때 다양한 문제에 적용이 가능하도록 일반 곡선 좌표계에서 식을 유도하였고, 수치해석을 위한 행렬식들을 함께 유도하였다. 개발된 해석 코드를 표면장력이 있는 기포 동역학 문제와 수중익에 의한 파도 발생 문제에 적용하여 타당한 결과를 얻을 수 있었다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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• pp.110-119
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• 2006

An accurate and cost efficient method PSE is used for the stability analysis of 2D or 3D compressible boundary layers. A highly accurate finite difference PSE code has been developed at a general curvilinear coordinate system using an implicit marching procedure to deal with a broad range of transition predictions problems. Evolution of disturbances in compressible flat plate boundary layers are studied for free-stream Mach numbers ranging from 0 to 1.5. The effect of mean-flow nonparallelism is found to be weak on two dimensional waves and strong on three dimensional waves. The maximum amplification rate increases monotonically with Mach number. The present PSE solutions are compared with previous numerical investigations and experimental results and are found to be in good agreement.