• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 춘계 학술대회논문집
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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.

• 한국수자원학회논문집
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• 제38권2호
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• pp.133-142
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• 2005

미세하게 부유된 입자(alumina(Al$_2$O$_3$), quartz(SiO$_2$))의 침전 농도를 물리-화학적(초기농도, pH, NaCl)인 영향을 고려하면서 연구하였다. 침강실험은 입자사이의 끌어당기는 힘 때문에 Flocculation(플록 형성)이 일으키는 초기농도와 NaCl의 증가가 중요한 영향을 미치며, 더욱이 미립자(alumina(Al$_2$O$_3$))의 농도-시간 곡선에 pH의 영향이 매우 큼을 보였다. 또한 정지수면 조건하에서 미립자의 침전 거동예측을 위한 수치 모델은 부정류 1차원 이송방정식에 의해 분석되었으며 양해법, 음해법, Crank-Nicolson 기법 및 유한차분법을 이용하였다. 수치모델은 평형을 이룬 농도변화까지 예측하였으며, 실험치의 비교분석을 통해 중앙차분법을 통한 Implicit 모형의 계산이 대체로 일치하였다.

• Journal of Theoretical and Applied Mechanics
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• 제3권1호
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• pp.45-65
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• 2002

A constitutive model on oorthotropic thermo-elasto-viscoplasticity for fiber-reinforced composite materials Is illustrated, and their thermomechanical responses are predicted with the fully-coupled finite element formulation. The unmixing-mixing scheme can be adopted with the multipartite matrix method as the constitutive model. Basic assumptions based upon the composite micromechanics are postulated, and the strain components of thermal expansion due to temperature change are included In the formulation. Also. more than two sets of mechanical variables, which represent the deformation states of multipartite matrix can be introduced arbitrarily. In particular, the unmixing-mixing scheme can be used with any well-known isotropic viscoplastic theory of the matrix material. The scheme unnecessitates the complex processes for developing an orthotropic viscoplastic theory. The governing equations based on fully-coupled thermomechanics are derived with constitutive arrangement by the unmixing-mixing concept. By considering some auxiliary conditions, the Initial-boundary value problem Is completely set up. As a tool of numerical analyses, the finite element method Is used with isoparametric Interpolation fer the displacement and the temperature fields. The equation of mutton and the energy conservation equation are spatially discretized, and then the time marching techniques such as the Newmark method and the Crank-Nicolson technique are applied. To solve the ultimate nonlinear simultaneous equations, a successive iteration algorithm is constructed with subincrementing technique. As a numerical study, a series of analyses are performed with the main focus on the thermomechanical coupling effect in composite materials. The progress of viscoplastic deformation, the stress-strain relation, and the temperature History are careful1y examined when composite laminates are subjected to repeated cyclic loading.

• International Journal of Naval Architecture and Ocean Engineering
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• 제9권4호
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• pp.429-438
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• 2017

Cranke-Nicolson scheme in native OpenFOAM source libraries was not able to provide 2nd order temporal accuracy of velocity and pressure since the volume flux of convective nonlinear terms was 1st accurate in time. In the present study the simplest way of getting the volume flux with 2nd order accuracy was proposed by using old fluxes. A possible numerical instability originated from an explicit estimation of volume fluxes could be handled by introducing a weighting factor which was determined by observing the ratio of the finally corrected volume flux to the intermediate volume flux at the previous step. The new calculation of volume fluxes was able to provide temporally accurate velocity and pressure with 2nd order. The improvement of temporal accuracy was validated by performing numerical simulations of 2D Taylor-Green vortex of which an exact solution was known and 2D vortex shedding from a circular cylinder.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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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.

• 대한기계학회논문집B
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• 제24권10호
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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).

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 1998년도 추계학술대회논문집:21세기에 대비한 지능형 통합항만관리
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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.

• 대한기계학회논문집A
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• 제24권8호
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• pp.2042-2049
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• 2000

This paper is concerned with the comparison of forging characteristics between forward and backward processes, through the three-dimensional finite element simulation, for the aluminum powder forging of engine pistons. Starting from the theoretical formulation of velocity and temperature fields in the sintered preform during the process, we examine the comparative distributions of relative density, effective stress and temperature as well as the variations of total forging load and total volume reduction. Through the comparative results, we find out that the forward method provides better forging characteristics than the backward method.

• East Asian mathematical journal
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• 제33권1호
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• pp.53-65
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• 2017

Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집B
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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.