• 오토저널
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• 제11권1호
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• pp.14-19
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• 1989

본 해설에서는 이와같은 SOlution-Adaptive-Grid 방법중 1982년 Blackbill과 Salzman에 의하여 제안된 변분법을 이용한 Solution Adaptive Grid 방법에 대한 기본방정식 그리고 계산방법들을 소개하고자 한다. 이 방법은 논리적 구조에 있어서 명확하고 2차원 3차원 문제에 쉽게 확장시켜 적용할 수 잇기 때문에 많은 연구자들에 의하여 채택되고 있다.

• Coupled systems mechanics
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• 제4권1호
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• pp.67-98
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• 2015

Numerical prediction of dynamic behavior of fully coupled saturated porous media is of great importance in many engineering problems. Specifically, static and dynamic response of soils - porous media with pores filled with fluid, such as air, water, etc. - can only be modeled properly using fully coupled approaches. Modeling and simulation of static and dynamic behavior of soils require significant Verification and Validation (V&V) procedures in order to build credibility and increase confidence in numerical results. By definition, Verification is essentially a mathematics issue and it provides evidence that the model is solved correctly, while Validation, being a physics issue, provides evidence that the right model is solved. This paper focuses on Verification procedure for fully coupled modeling and simulation of porous media. Therefore, a complete Solution Verification suite has been developed consisting of analytical solutions for both static and dynamic problems of porous media, in time domain. Verification for fully coupled modeling and simulation of porous media has been performed through comparison of the numerical solutions with the analytical ones. Modeling and simulation is based on the so called, u-p-U formulation. Of particular interest are numerical dispersion effects which determine the level of numerical accuracy. These effects are investigated in detail, in an effort to suggest a compromise between numerical error and computational cost.

• Structural Engineering and Mechanics
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• 제81권4호
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• pp.523-527
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• 2022

The objective of this study is to simulate the flow in pipes with various boundary conditions. Free-pressure fluid model, is used in the pipe based on Navier-Stokes equation. The models are solved by using the numerical method. A problem called "stability of pipes" is used in order to compare frequency and critical fluid velocity. When the initial conditions of problem satisfied the instability conditions, the free-pressure model could accurately predict discontinuities in the solution field. Employing nonlinear strains-displacements, stress-strain energy method the governing equations were derived using Hamilton's principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The results of this paper are analyzed by hyperbolic numerical method. Results show that the level of numerical diffusion in the solution field and the range of well-posedness are two important criteria for selecting the two-fluid models. The solutions for predicting the flow variables is approximately equal to the two-pressure model 2. Therefore, the predicted pressure changes profile in the two-pressure model is more consistent with actual physics. Therefore, in numerical modeling of gas-liquid two-phase flows in the vertical pipe, the present model can be applied.

• Wind and Structures
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• 제7권1호
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• pp.13-28
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• 2004

A method of numerical analysis without conducting 3D wind tunnel model tests was examined in our previous study for predicting vortex-induced oscillation of bridge girders with span-wise varying geometry. The aerodynamic damping forces measured for plural wind tunnel 2D models were used in the analysis. A further study was conducted to examine the precision of solution obtained by this method. First, the responses of vortex-induced oscillation of two rocking models and a taut-strip bridge girder model with span-wise varying geometry were measured. Next, the responses of these models were numerically analyzed by means of this method, and then a comparison was made between the obtained $Vr-A-{\delta}_a$ contour diagram of each 3D model in the wind tunnel test and the diagram in the numerical analysis. Since close correlations were observed between each two $Vr-A-{\delta}_a$diagrams obtained in the model test and in the analysis in cases where the 3D model did not have strong three-dimensionality, our findings revealed that the predicted solution proved to be reasonably accurate.

• Nuclear Engineering and Technology
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• 제45권2호
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• pp.191-202
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• 2013

A numerical analysis of thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (~300 seconds). However, transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A nearly homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates. This discrepancy may be due to the shortcoming of the turbulence models available in the CFX-13 code for a natural convection flow with thermal stratification.

• 한국정밀공학회지
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• 제12권5호
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• pp.57-68
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• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• 대한기계학회논문집
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• 제15권1호
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• pp.120-126
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• 1991

본 연구에서는 Kawabata가 제안한 직접수치해법(direct numerical solution method)을 확대하여 윤활표면으 국부 회소가스 효과(local rarefaction effect)로 인 한 공기분자의 벽면 미끄름 현상을 고려한 지배방정식을 Navier-Stokes방정식으로 부 터 유도하고 이를 2차원 유동의 경우까지 확대하여 극소틈새와 높은 압축성 계수를 갖 는 경우에 적용하고 그 결과를 기존의 수정된 레이노래즈 방정식의 해석결과와 비교하 고자 한다.

• Geomechanics and Engineering
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• 제15권3호
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• pp.889-898
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• 2018

Backfilling of mine stopes with waste rocks or tailings is commonly done to enhance ground stability. It is also an alternative for mining wastes disposal. A successful application of underground backfilling requires an accurate evaluation of the stress distribution in stopes. Over the years, various analytical solutions have been proposed to assess these stresses. Most of them were based on the arching theory, considering uniform stresses across horizontal layer elements. The vertical and horizontal stresses in vertical stopes are principal stresses only along the vertical center line, but not close to the walls where there is rotation of the principal stresses. A few solutions use arc layer elements that follow the iso-contours of the minor principal stresses, based on numerical solutions. In this paper, a modified analytical solution is developed for the stresses in vertical backfilled stopes, considering a circular arc distribution. The proposed solution is calibrated with a few numerical modeling results and then validated by additional numerical simulations under different conditions.

• 대한기계학회논문집A
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• 제27권9호
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• pp.1555-1561
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• 2003

Finite element analysis using modern constitutive equation is one of the most general tools to simulate the deformation behavior and to predict the life of the structure. Constitutive equation becomes complicated so as to predict the material behavior more accurately than the classical models. Because of the complexity of constitutive model, numerical treatment becomes so difficult that the calculation should be verified carefully. One-element tests, simple tension or simple shear, are usually used to verify the accuracy of finite element analysis using complicated constitutive model. Since this test is mainly focused on the time integration scheme, it is also necessary to verify the equilibrium iteration using material stiffness matrix and to compare FE results with solution of structures. In this investigation, viscoplastic solution of thick walled cylinder was derived considering axial constraints and was compared with the finite element analysis. All the numerical solutions showed a good coincidence with FE results. This numerical solution can be used as a verification tool for newly developed FE code with complicated constitutive model.

• 대한조선학회논문집
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• 제42권2호
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• pp.113-123
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• 2005

A higher order panel method based on B-spline representation for both the geometry and the solution is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then shown to be evaluated using conventional numerical quadrature. By selecting a proper order for numerical quadrature, the accuracy of the present method can be increased to the machine limit. The far- and near-field influences are shown to be evaluated based on the same far-field approximation, but the near-field solution requires subdividing the panels into smaller subpanels continuously, which can be effectively implemented due to the B-spline representation of the geometry. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution on the blade surface, including very close to the tip and trailing edge regions, with far fewer panels than existing low order panel methods.