• Title/Summary/Keyword: Euler explicit method

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Real Time Textile Animation Using Fuzzy Inference (퍼지추론을 적용한 직물 애니메이션)

  • Hwang, Seon-Min;Song, Bok-Hee;Yun, Han-Kyung
    • The Journal of the Korea Contents Association
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    • v.11 no.9
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    • pp.1-8
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    • 2011
  • A fuzzy inference technique for real-time textile animation without integration at textile model based Mass-Spring model is introduced. Until now many techniques have used the Mass-Spring model to describe elastically deformable objects like textile. A textile object is able to represent as a deformable surface composed of spring and masses, the movement of textile surface which is analysed through the numerical integration by the fundamental law of dynamics such as Hooke's law. However, the integration methods have 'instability problems' if the explicit Euler's method is applied or 'large amounts of calculation' if the implicit Euler's method is applied. A simple and fast animation technique for Mass-Spring model of a textile with fuzzy inference is proposed. The stabilized simulation result is obtained the state of each mass-point in real-time for the n of mass-points by a relatively simple calculation.

Analysis of Viscous Free Surface Flow around a Ship by a Level-set Method

  • Park, Il-Ryong;Chun, Ho-Hwan
    • Journal of Ship and Ocean Technology
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    • v.6 no.2
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    • pp.37-50
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    • 2002
  • In the present numerical simulation of viscous free surface flow around a ship, two-fluids in-compressible Reynolds-averaged Navier-Stokes equations with the standard $\textsc{k}-\varepsilon$turbulence model are discretized on a regular grid by using a finite volume method. A local level-set method is introduced for capturing the free surface movement and the influence of the viscous layer and dynamic boundary condition of the free surface are implicitly considered. Partial differential equations in the level-set method are discretized with second order ENO scheme and explicit Euler scheme in the space and time integration, respectively. The computational results for the Series-60 model with $C_B=0.6$ show a good agreement with the experimental data, but more validation studies for commercial complicated hull forms are necessary.

DEVELOPMENT OF A NON-STANDARD FINITE DIFFERENCE METHOD FOR SOLVING A FRACTIONAL DECAY MODEL

  • SAID AL KATHIRI;EIHAB BASHIER;NUR NADIAH ABD HAMID;NORSHAFIRA RAMLI
    • Journal of applied mathematics & informatics
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    • v.42 no.3
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    • pp.695-708
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    • 2024
  • In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

Numerical Analytic Study on Internal Flow Characteristics of a PCV valve (PCV 밸브 내부 유동특성에 관한 수치해석적 연구)

  • Lee, Jong-Hoon;Lee, Yeon-Won;Kim, Jae-Hwan
    • 한국가시화정보학회:학술대회논문집
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    • 2005.12a
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    • pp.111-116
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    • 2005
  • An automobile engine has the Positive Crankcase Ventilation system (PCV system) for preventing air pollution as the environmental problem is important In this system, a PCV valve is the most important component to control the flow rate of Blowby gas which is generated by various engine powers. But, in the working place, the design of a PCV valve is very difficult because of interaction between fluid and solid motions. In this study, we investigated fluid flow characteristics using re-meshing method of a CFD technique to simulate spool behavior. As the results, a spool is periodically oscillated with time and is largely oscillated in proportion to the differential pressure between inlet and outlet. And, although the velocity at the orifice increases with the differential pressure, the flow rate of the outlet decreases. This research may give PCV designers visual flow information to help them

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BIVARIATE NUMERICAL MODELING OF THE FLOW THROUGH POROUS SOIL

  • S. JELTI;A. CHARHABIL;A. SERGHINI;A. ELHAJAJI;J. EL GHORDAF
    • Journal of applied mathematics & informatics
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    • v.41 no.2
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    • pp.295-309
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    • 2023
  • The Richards' equation attracts the attention of several scientific researchers due to its importance in the hydrogeology field especially porous soil. This work presents a numerical method to solve the two dimensional Richards' equation. The pressure form and the mixed form of Richards' equation are solved numerically using a bivariate diamond finite volumes scheme. Euler explicit scheme is used for the time discretization. Different test cases are done to validate the accuracy and the efficiency of our numerical model and to compare the possible numerical strategies. We started with a first simple test case of Richards' pressure form where the hydraulic capacity and the hydraulic conductivity are taken constant and then a second test case where the hydrodynamics parameters are linear variables. Finally, a third test case where the soil parameters are taken according the Van Gunchten empirical model is presented.

A New Numerical Method for Solving Differential Equation by Quadratic Approximation (포물선 근사법에 의한 상태방정식의 새로운 수치해석적 접근법에 관한 연구)

  • Lee, Jong-Gi;Kwon, Yong-Jun;Choi, Byoung-Kon;Moon, Young-Hyun
    • Proceedings of the KIEE Conference
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    • 2003.07a
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    • pp.107-109
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    • 2003
  • 전력계통의 과도 안정도 해석의 접근방법에는 SI(Simultaneous Implicit)법과 PE(Partitioned Explicit)법 두 가지방법을 사용해오고 있다. SI법에는 Trapezoidal법 등이 있고, PE법에는 Runge-Kutta법, Euler법등이 사용되고 있다. SI법인 Trapezoidal법은 PE법의 Runge-Kutta법 또는 Euler법에 비해 시간간격을 크게 해서 계산속도를 줄일 수 있다는 장점이 있지만, 정화도면에서는 신뢰한 수 없는 단점이 있다. 이 논문에서는 포물선 사법을 이용하여 Trapezoidal법의 정확도를 개선학 수 있는 방법을 제시하고 명확한 수학적 증명을 통해 타당성을 보여준다. 연속함수와 불연속함수에 대해서 Runge-Kutta법과 Trapezoidal법과 제안한 방법을 적용시켜서 제안한 방법의 정화함을 보여준다.

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Analytical solutions for bending of transversely or axially FG nonlocal beams

  • Nguyen, Ngoc-Tuan;Kim, Nam-Il;Lee, Jaehong
    • Steel and Composite Structures
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    • v.17 no.5
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    • pp.641-665
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    • 2014
  • This paper presents the analytical solutions for the size-dependent static analysis of the functionally graded (FG) beams with various boundary conditions based on the nonlocal continuum model. The nonlocal behavior is described by the differential constitutive model of Eringen, which enables to this model to become effective in the analysis and design of nanostructures. The elastic modulus of beam is assumed to vary through the thickness or longitudinal directions according to the power law. The governing equations are derived by using the nonlocal continuum theory incorporated with Euler-Bernoulli beam theory. The explicit solutions are derived for the static behavior of the transversely or axially FG beams with various boundary conditions. The verification of the model is obtained by comparing the current results with previously published works and a good agreement is observed. Numerical results are presented to show the significance of the nonlocal effect, the material distribution profile, the boundary conditions, and the length of beams on the bending behavior of nonlocal FG beams.

Optimum design of shape and size of truss structures via a new approximation method

  • Ahmadvand, Hosein;Habibi, Alireza
    • Structural Engineering and Mechanics
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    • v.76 no.6
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    • pp.799-821
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    • 2020
  • The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.

Numerical Analysis of Steel-strengthened Concrete Panels Exposed to Effects of Blast Wave and Fragment Impact Load Using Multi-solver Coupling (폭풍파 및 파편 충돌에 대한 강판보강 콘크리트 패널의 복합적 수치해석)

  • Yun, Sung-Hwan;Park, Taehyo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.31 no.1A
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    • pp.25-33
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    • 2011
  • The impact damage behavior of steel-strengthened concrete panels exposed to explosive loading is investigated. Since real explosion experiments require the vast costs to facilities as well as the blast and impact damage mechanisms are too complicated, numerical analysis has lately become a subject of special attention. However, for engineering problems involving blast wave and fragment impact, there is no single numerical method that is appropriate to the various problems. In order to evaluate the retrofit performance of a steel-strengthened concrete panel subject to blast wave and fragment impact loading, an explicit analysis program, AUTODYN is used in this work. The multi-solver coupling methods such as Euler-Lagrange and SPH-Lagrange coupling method in order to improve efficiency and accuracy of numerical analysis is implemented. The simplified and idealized two dimensional and axisymmetric models are used in order to obtain a reasonable computation running time. As a result of the analysis, concrete panels subject to either blast wave or fragment impact loading without the steel plate are shown the scabbing and perforation. The perforation can be prevented by concrete panels reinforced with steel plate. The numerical results show good agreement with the results of the experiments.

A STUDY ON INTERNAL FLOW CHARACTERISTICS OF PCV VALVE ACCORDING TO SPOOL DYNAMIC BEHAVIOR (PCV 밸브의 스풀 동적거동에 따른 내부유동 특성에 관한 연구)

  • Lee J.H.;Lee Y.W.;Kim J.H.
    • 한국전산유체공학회:학술대회논문집
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    • 2005.10a
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    • pp.223-227
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    • 2005
  • A PCV valve is a part to control the flow rate of Blowby gas in a PCV system. A PCV system re-burns Blowby gas with fuel in a combustion chamber. Some gas enters to a crankcase room through the gap between piston ring and engine cylinder wall. This gas si called 'Blowby gas'. This gas causes many problems. In environmental view, Blowby gas includes about $25\~35\%$ hydrocarbon{HC) of total generated HC in an automobile. Hydrocarbon is a very harmful pollutant element in our life. In mechanical view, Blowby gas has some reaction with lubricant oil of crankcase room. Then, this causes lubricant oil contamination, crankcase corrosion and a decrease fo engine efficiency. Consequently, Blowby gas must be eliminated from a crankcase room. In this study, we simulated internal flow characteristics in a PCV valve according to spool dynamic behavior using local remeshing method And, we programmed our sub routine to simulate a spool dynamic motion. As results, spool dynamic behavior is periodically oscillated by the relationship between fluid force and elastic force of spring. And its magnitude is linearly increased by the differential pressure between inlet and outlet. Also, as spool is largely moved, flow area is suddenly decreased at orifice. For this reason, flow velocity is rapidly decreased by viscous effect.

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