• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.12
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• pp.1570-1579
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• 2000

Finite element analysis of fluid flow with moving free surface has been carried out in two and tree dimensions. The new VOF-based numerical algorithm that has been proposed by the present authors was applied to several 2-D and 3-D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools that have been newly introduced by the present authots; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2-D and 3-D cavity filling and sloshing problems, which demonstrated versatility and effectiveness of the new free surface tracking scheme as well as the overall solution procedure. The proposed numerical algorithm resolved successfully the interacting free surface with each other. The simulated results demonstrated the applicability of proposed numerical algorithm to the practical problems of large free surface motion. Also, it has been demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non-uniform grid systems and can be extended to the 3-D free surface flow problem without additional efforts.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.392-397
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• 2001

A numerical study is performed to investigate the interaction between subsonic axial turbine blade boundary layer and periodically oncoming rotor induced wakes. An implicit scheme for solving the compressible Navier-Stokes equation is developed, which adopts a 4th-order compact difference for spatial discretiztion, a 2nd order Crank-Nicolson scheme for temporal discretization and the dynamic eddy viscosity model as the subgrid scale model. The efficiency and the accuracy of the proposed method are verified by applying to some benchmark problems such as laminar cylinder flow, laminar airfoil cascade flow and a transitional flat plate boundary layer flow. Computational results show good agreements with previous experimental and numerical results. Finally, flow through a stator cascade is simulated at $Re = 7.5{\times}10^5$ without free-stream turbulence intensity. The velocity fields and skin friction coefficients in the transitional region show similar trends with previous boundary layer natural transition.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.1
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• pp.1-10
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• 2010

In the present paper, a numerical method based on the constraint interpolation profile (CIP) method is applied for simulating two-dimensional violent sloshing problems. The free surface boundary value problem is considered as a multiphase problem which includes water and air. A stationary Cartesian grid system is adopted, and an interface capturing method is used to trace the shape of free surface profile. The CIP combined unified procedure (CCUP) scheme is applied for flow solver, and the tangent of hyperbola for interface capturing (THINC) scheme is used for interface capturing. Numerical simulations have been carried out for partially-filled 2D tanks under forced sway and roll motions at various filling depths and frequencies. The computational results are compared with experiments and/or the other numerical results to validate the present numerical method.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.237-255
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• 2013

In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• International Journal of Ocean System Engineering
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• v.1 no.3
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• pp.136-143
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• 2011

In this paper, three-dimensional free-surface flows are simulated by using two different numerical methods, the constrained interpolation profile (CIP)-based and finite volume (FV)-based methods. In the CIP-based method, the governing equations are solved on stationary staggered Cartesian grids by a finite difference method, and an immersed boundary technique is applied to deal with wave-body interactions. In the FV-based method, the governing equations are solved by applying collocated finite volume discretization, and body-fitted meshes are used. A free-surface boundary is considered as the interface of the multi-phase flow with air and water, and a volumeof-fluid (VOF) approach is applied to trace the free surface. Among many variations of the VOF-type method, the tangent of hyperbola for interface capturing (THINC) and the compressive interface capturing scheme for arbitrary meshes (CICSAM) techniques are used in the CIP-based method and FV-based method, respectively. Numerical simulations have been carried out for dam-breaking and wave-body interaction problems. The computational results of the two methods are compared with experimental data and their differences are observed.

• Journal of Ocean Engineering and Technology
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• v.21 no.6
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• pp.53-58
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• 2007

A particle method, recognized as one of gridless methods, has been developed to investigate non-linear free-surface motions interacting with structures. This method is more feasible and effective than conventional grid methods for solving flow fieldswith complicated boundary shapes. The method consists of particle interaction models representing pressure gradient, diffusion, incompressibility, and the free-surface boundary conditions without grids. In the present study, broken dam problems with various viscosity values are simulated to validate the developed method.

• Steel and Composite Structures
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• v.39 no.5
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• pp.493-509
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• 2021

There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gateaux differential derivative operator. Thanks to the Gateaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2546-2554
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• 1996

In order to investigate the characteristics of sound-structure interaction problems, we modeled a rectangular cavity and the flexible wall of the cavity. Because the governing equations of motion are coupled through velocity terms, we could redefine them using the velocity potential. We calculated the natural frequencies of plate using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz Method. As the result, comparisons of theory and experiment show good agreement. and using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz method show useful method for sound-structure interaction problems too.