• Proceedings of the KSME Conference
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• 2000.04b
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• pp.704-708
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• 2000

A new efficient numerical method for computing unsteady, incompressible flows, DRANS (Decoupled Reynolds-Averaged Navier-Stokes), is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used fer both the diffusion and convection terms. is adopted. Based on decomposition method, the velocity-turbulent quantity decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully-implicit time advancement scheme. Since the iterative procedures for the momentum, ${\kappa}\;and\;{\varepsilon}$ equations are not required, the components decouplings bring fourth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to turbulent boundary layer with local forcing.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.910-915
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• 2003

A Navier-Stokes equation solver for incompressible viscous flows with free surface is developed and tested. This is based upon a fractional time step method and a non-staggered finite volume formulation for unstructured meshes. For time advancement scheme, Adams -Bashforth method for convective term and Crank-Nicolson method for diffusive term are applied. The interface between two fluids with different fluid properties is tracked with Piecewise Linear Interface Calculation(PLIC) Volume-of-Fluid(VOF) methods. Computational results are presented for some test problems: the broken dam, the sloshing in a rectangular tank, the filling of a cylindrical tank.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.123-135
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• 2015

In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.71-76
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• 2004

An extension of our recently developed locally linear reconstruction scheme to 2 dimensional incompressible flow solver is presented. The solver is based on a semi-implicit fractional step method in which the convective term is discretized by Adams-Bashforth method and the diffusion term by Crank-Nicolson method. Several numerical examples are tested to demonstrate the mesh type independent accuracy of the solver, which include decaying vortex flow, square cavity flow, and flow around a circular cylinder. The above examples are solved on quadrilateral or hybrid meshes. For all numerical examples, we obtained reasonable results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1317-1325
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• 2000

A new efficient numerical method for computing three-dimensional, unsteady, incompressible flows is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used for both the diffusion and convection terms, is adopted. Based on an approximate block LU decomposition method, the velocity -pressure decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully -implicit time advancement scheme. Since the iterative procedures for the momentum equations are not required, the velocity components decouplings bring forth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to minimal channel flow unit with DNS (Direct Numerical Simulation).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.6 s.237
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• pp.703-710
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• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.121-137
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• 2022

In this paper, we investigate an efficient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 1998.10a
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• pp.201-209
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• 1998

The propagation of water waves over irregular bottom bathymetry and around islands involves many process. In this study of numerical model is developed current in water of varying depth. The method used is splitting method and minimax approximation. This numerical method used is Crank-Nicolson scheme. This model is applied to Vincent shoal and compared with laboratory data. The results agreed well with laboratory data. The results agreed well with laboratory data. Current effect is considered in this study. So, the model is used for the estimation of rip current in the slowly varying topography.

• Journal of Korean Port Research
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• v.12 no.2
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• pp.281-290
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• 1998

The propagation of water waves over irregular bottom bathymetry and around islands involves many process-shoaling, refraction, energy dissipation and diffraction. Numerical model in this study is developed with the mild slope equation to investigate wave transformation in water of varying depth and combined waves and a current. The method used is splitting method and minimax approximation. The numerical method used in this study is Crank-Nicolson scheme in the FDM. This model is applied to Vincent shoal and compared with laboratory experimental data. The results agreed well with laboratory data. Current effect is considered in this study. This model can be used for the estimation of rip current in the slowly varying topography.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.301-313
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• 2009

This paper presents a Finite Element Method (FEM) application to thermal study of natural three layers of human dermal parts of varying properties. This paper carries out investigation of temperature distributions in these layers namely epidermis, dermis and under lying tissue layer. It is assumed that the outer skin is exposed to atmosphere and the loss of heat due to convection, radiation and evaporation of water have also been taken into account. The computations are carried out for one dimensional unsteady state case and the shape functions in dermal parts have been considered to be quadratic. A Finite Element scheme that uses the Crank-Nicolson method is used to solve the problem and the results computed have been exhibited graphically.