• 한국방재학회:학술대회논문집
• /
• 한국방재학회 2007년도 정기총회 및 학술발표대회
• /
• pp.181-185
• /
• 2007

A free-surface correction(FSC) method is presented to solve the 3-D shallow water equations. Using the mode splitting process, FSC method can simulate shallow water flows under the hydrostatic assumption. For the hydrostatic pressure calculation, the momentum equations are firstly discretized using a semi-implicit scheme over the vertical direction leading to the tri-diagonal matrix systems. A semi-implicit scheme has been adopted to reduce the numerical instability caused by relatively small vertical length scale compare to horizontal one. and, as the free surface correction step the final horizontal velocity fields are corrected after the final surface elevations are obtained. Finally, the vertical final velocity fields can be calculated from the continuity equation. The numerical model is applied to the calculation of the simulation of flow fields in a rectangular open channel with the tidal influence. The comparisons with the analytical solutions show overall good agreements between the numerical results and analytical solutions.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1129-1141
• /
• 2011

In this paper, a class of large time-stepping method based on the finite element discretization for the Cahn-Hilliard equation with the Neumann boundary conditions is developed. The equation is discretized by finite element method in space and semi-implicit schemes in time. For the first order fully discrete scheme, convergence property is investigated by using finite element analysis. Numerical experiment is presented, which demonstrates the effectiveness of the large time-stepping approaches.

• Journal of Mechanical Science and Technology
• /
• 제16권5호
• /
• pp.720-731
• /
• 2002

Flow with moving free surfaces is analyzed with an the Eulerian coordinate system. This study proposes a semi-implicit filling algorithm using VOF in which the PLIC (Piecewise Linear Interface Calculation) -type interface reconstruction method and the donor-acceptor-type front advancing scheme are adopted. Also, a new scheme using extrapolation of the stream function is proposed to find the velocity of the node that newly enters the computational domain. The effect of wall boundary conditions on the flow field and temperature field is examined by numerically solving a two-dimensional casting process.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2007년도 추계 학술대회논문집
• /
• pp.243-248
• /
• 2007

A three-dimensional (3D) unstructured hydrodynamic solver for transient two-phase flows has been developed. A two-fluid three-field model was adopted for the two-phase flows. The three fields represent a continuous liquid, an entrained liquid, and a vapour field. The hydrodynamic solver is for the 3D component of a nuclear system code and the component-scale analysis tools for transient two-phase flows. The finite volume method and unstructured grid are adopted, which are useful for the flows in a complicated geometry. The semi-implicit ICE (Implicit Continuous-fluid Eulerian) numerical scheme has been adapted to the unstructured non-staggered grid. This paper presents the numerical method and the preliminary results of the calculations. The results show that the numerical scheme is robust and predicts the phase change and the flow transitions due to boiling and flashing problems well.

• Nuclear Engineering and Technology
• /
• 제16권2호
• /
• pp.47-57
• /
• 1984

2상유동을 해석하기 위한 3차원 코드인 THERMIT-6S의 미분 방정식을 세우기 위해, 수학적으로 정확하게 유도된 시간과 공간에 대해 평균한 보존 방정식을 단순화했다. 미분 방정식을 불연속화(discretization)하여 THERMIT-6S의 차분방정식을 얻는다. First-order spatial scheme, donor cell method, 그리고, staggered mesh layout을 써서 공간에 대한 불연속화를 한다. 그리고 시간에 대한 불연속화는 first-order semi-implicit scheme으로써, sonic terms와 국부적인 전달 현상에 관계되는 항들은 implicit하게 그리고 대류 전달 항들은 explicit하게 취급한다. 이렇게 얻어진 방정식들은Newton-Raphson 방법으로 선형화된다. 축소된 압력 방정식을 만들기 위해 모든 변수들이 mesh cells사이에서 단지 압력 변수를 통해서만 결부되도록, 선형화된 방정식들을 처리한다. OPERA-15 실험을 수치해석적으로 모의실험하여 본 결과, THERMIT-6S가 flow coastdown, 역류, 유체진동(flow oscillation) 등을 포함하고, sodium boiling 후의 원자로내의 변화를 예측하는데 매우 유효하다는 것이 밝혀졌다.

• Geomechanics and Engineering
• /
• 제25권4호
• /
• pp.267-273
• /
• 2021

In this work, we compare the analytical solutions with the numerical solutions for photothermal interactions in semiconductor medium containing cylindrical cavity. This paper is devoted to a study of the photothermal interactions in semiconductor medium in the context of the coupled photo-thermal model. The basic equations are formulated in the domain of Laplace transform and the eigenvalue scheme are used to get the analytical solutions. The numerical solution is obtained by using the implicit finite difference method (IFDM). A comparison between the analytical solution and the numerical solutions are obtained. It is found that the implicit finite difference method (IFDM) is applicable, simple and efficient for such problems.

• Journal of Mechanical Science and Technology
• /
• 제20권10호
• /
• pp.1773-1778
• /
• 2006

Steady-state natural convection heat transfer characteristics from cylinders in a multiply-connected bounded region are clarified. A spectral finite difference scheme (spectral decomposition of the system of partial differential equations, semi-implicit time integration) is applied in numerical analysis, with a boundary-fitted conformal coordinate system through a Jacobian elliptic function with a successive transformation to formulate a system of governing equations in terms of a stream function, vorticity and temperature. Multiplicity of the domain is expressed explicitly.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제8권4호
• /
• pp.320-329
• /
• 2016

An implicit method of solving the six degree-of-freedom rigid body motion equations based on the second order Adams-Bashforth-Moulten method was utilised as an improvement over the leapfrog scheme by making modifications to the rigid body motion solver libraries directly. The implementation will depend on predictor-corrector steps still residing within the hybrid Pressure Implicit with Splitting of Operators - Semi-Implicit Method for Pressure Linked Equations (PIMPLE) outer corrector loops to ensure strong coupling between fluid and motion. Aitken's under-relaxation is also introduced in this study to optimise the convergence rate and stability of the coupled solver. The resulting coupled solver ran on a free floating object tutorial test case when converged matches the original solver. It further allows a varying 70%-80% reduction in simulation times compared using a fixed under-relaxation to achieve the required stability.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권3호
• /
• pp.197-207
• /
• 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.

• 대한토목학회논문집
• /
• 제14권5호
• /
• pp.1145-1158
• /
• 1994

물의 유동(流動)에 관한 계산상 효율성(效率性)을 갖는 자유수면(自由水面)을 고려한 3차원(次元) 유한차분(有限差分) 수직모형(數値模型)을 개발하였다. 수직모형(數値模型)은 연직방향(鉛直方向)에 대해 정규화(正規化)한 좌표(座標)(${\sigma}$-coordinate)를 사용하며, 시간(時間) 적분방법(積分方法)으로는 반음해법(半陰解法)(semi-implicit)을 사용하여 계산시간(計算時間)의 효율성(效率性)을 도모하였다. 모드분리(mode-splitting)개념을 도입하여 내부모드(internal mode)에 대해서는 양해법(陽解法)을 사용하였으며, 외부모드(external mode)는 수평방향(水平方向) 운동량방정식(運動量方程式)들과 연속방정식(連續方程式)의 차분식(差分式)으로부터 구한 타원형(楕圓型) 차분방정식(差分方程式)을 SOR방법에 의하여 해석하였다. 이와 같은 방법은 계산(計算) 시간간격(詩間間隔)이 표면(表面) 중력파(重力波)에 대한 CFL(Courant-Fredrich-Lewy)조건에 의해 제약을 받지 않아 계산시간(計算時間)의 효율성을 도모할 수 있다. 개발된 모형은 1차원(次元) 수로(水路)에서 취송유(吹送流)의 연직분포(鉛直分布)에 대한 해석해(解析解)와 비교(比較) 및 연직(鉛直) 가변격자(可變格子)의 도입에 따른 오차분석(誤差分析) 정사각형(正四角形) 호수(湖水)에서 취송유(吹送流) 계산(計算) 및 차분화(差分化) 상수(常數)들의 민감도(敏感度) 분석(分析)을 수행하였다.