• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.12
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• pp.1555-1569
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• 2000

Numerical simulation of fluid flow with moving free surface has been carried out. For the free surface flow, a VOF(Volume of Fluid)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface tracking algorithm based on the donor-acceptor scheme has been presented. Novel features of the proposed algorithm are characterized as two numerical tools; 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 algorithm can be easily implemented in any irregular non-uniform grid systems that are usual in finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3-D free surface flow problem without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the SUPG(streamline upwind/Petrov-Galerkin) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface tracking scheme and explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

• International Journal of CAD/CAM
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• v.13 no.1
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• pp.1-11
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• 2013

Just by adjusting the control points iteratively, progressive iterative approximation (PIA) presents an intuitive and straightforward scheme such that the resulting limit curve (surface) can interpolate the original data points. In order to obtain more flexibility, adjusting only a subset of the control points, a new method called local progressive iterative approximation (LPIA) has also been proposed. But to this day, there are two problems about PIA and LPIA: (1) Only an approximation process is discussed, but the accurate convergence curves (surfaces) are not given. (2) In order to obtain an interpolating curve (surface) with high accuracy, recursion computations are needed time after time, which result in a large workload. To overcome these limitations, this paper gives an explicit matrix expression of the control points of the limit curve (surface) by the PIA or LPIA method, and proves that the column vector consisting of the control points of the PIA's limit curve (or surface) can be obtained by multiplying the column vector consisting of the original data points on the left by the inverse matrix of the collocation matrix (or the Kronecker product of the collocation matrices in two direction) of the blending basis at the parametric values chosen by the original data points. Analogously, the control points of the LPIA's limit curve (or surface) can also be calculated by one-step. Furthermore, the $G^1$ joining conditions between two adjacent limit curves obtained from two neighboring data points sets are derived. Finally, a simple LPIA method is given to make the given tangential conditions at the endpoints can be satisfied by the limit curve.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.539-546
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• 2003

The numerical model of the flow analysis by finite element technique is described. The Galerkin method is employed for spatial discretization Two step explicit finite element scheme is used to discretize the time function, which has advantage in problems treating large numbers of elements and unsteady state. Two dimensional hydrodynamic model considering moving boundary condition is developed. Also it applied flow model which develop on flow portion of ideal fluid in the model flume and verified, and the results of this study confirm the efficiency of moving boundary treatment in Jeju harbor. The computed results have shown the good adaptability of moving boundary condition From these studies, it can be concluded that the present method is a useful and effective tool in tidal flow analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.19-30
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• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• The KSFM Journal of Fluid Machinery
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• v.3 no.3 s.8
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• pp.7-11
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• 2000

A numerical study based on the three-dimensional thin-layer Navier-Stokes solver is carried out to analyze the flowfield through a single stage transonic compressor. Explicit fout-step Runge-Kutta scheme with spatially variable time step and implicit residual smoothing is used. The governing equations we discretized with explcit finite difference method. Mired-out average method is used at the interface between rotor and stator. And, an artificial dissipation model is used to assure the stability of solution. The results with k-w turbulence model were compared to the results with Baldwin-Lomax model, and physical phenomena of transonic compressor are presented. The two turbulence models give the results that show reasonably good agreements with experimental data.

• 유체기계공업학회:학술대회논문집
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• 1999.12a
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• pp.27-32
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• 1999

A numerical study based on the three-dimensional thin-layer Navier-Stokes solver is carried out to analyze the flowfield through a single stage transonic compressor. Explicit four-step Runge-Kutta scheme with spatially variable time step and implicit residual smoothing is used. The governing equations are discretized with exploit finite difference method. Mixed-out average method is used at the interface between rotor and stator. And, an artificial dissipation model is used to assure the stability of solution. The results with k-$\omega$ turbulence model were compared to the results with Baldwin-Lomax model, and physical phenomena of transonic compressor are presented. The two turbulence models give the results that show reasonably good agreements with experimental data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.197-207
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• 2013

The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.

• Journal of Sensor Science and Technology
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• v.28 no.3
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• pp.182-186
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• 2019

When a camera is employed for 3D sensing, accurate camera calibration is vital as it is a prerequisite for the subsequent steps of the sensing process. Camera calibration is usually performed by complex mathematical modeling and geometric analysis. On the other contrary, data learning using an artificial neural network can establish a transformation relation between the 3D space and the 2D camera image without explicit camera modeling. However, a neural network requires a large amount of accurate data for its learning. A significantly large amount of time and work using a precise system setup is needed to collect extensive data accurately in practice. In this study, we propose a two-step neural calibration method that is effective when only a small amount of learning data is available. In the first step, the camera projection transformation matrix is determined using the limited available data. In the second step, the transformation matrix is used for generating a large amount of synthetic data, and the neural network is trained using the generated data. Results of simulation study have shown that the proposed method as valid and effective.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.7 s.94
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• pp.1700-1709
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• 1993

The stepped specimen which is subjected to step loading is modeled to study the initiation and growth of adiabatic shear band using explicit time integration finite element method. Three different clearance sizes are tested. The material model for the stepped specimen includes effects of strain hardening, strain rate hardening and thermal softening. It is found that the material inside the fully grown adiabatic shear band experiences three phase of deformation, (1) homogeneous deformation phase, (2) initiation/incubation phase, and (3) fast growth phase. The second phase of deformation is initiated after sudden shear stress drop which occurs at the same time regardless of the clearance size. The incubation time prior to fast growth phase increases, as the clearance size of the stepped specimen increases. Whereas, after incubation period, the growth rate of the adiabatic shear band decreases, as the clearance size decreases. It is also found that two adiabatic shear band may develop instead of one for the smaller clearance size.

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.683-695
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• 2002

The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.