• Structural Engineering and Mechanics
• /
• v.17 no.6
• /
• pp.735-749
• /
• 2004

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

• International Journal of Aeronautical and Space Sciences
• /
• v.18 no.4
• /
• pp.816-826
• /
• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• Journal of IKEEE
• /
• v.23 no.3
• /
• pp.817-825
• /
• 2019

Difference equation is useful for control algorithm in the microprocessor. To approximate a derivative values from sampled data, it is used the methods of forward, backward and central differences. The key of computing discrete derivative values is the finite difference coefficient. The focus of this paper is a new approach method of finite difference formula. And we apply the proposed method to the recursive least squares(RLS) algorithm.

• Journal of computational fluids engineering
• /
• v.11 no.1 s.32
• /
• pp.36-42
• /
• 2006

The existing numerical approximations of convection flux, especially the spatial higher-order difference schemes, in unstructured cell-centered finite volume methods are examined in detail with each other and evaluated with respect to the accuracy through their application to a 2-D benchmark problem. Six higher-order schemes are examined, which include two second-order upwind schemes, two central difference schemes and two hybrid schemes. It is found that the 2nd-order upwind scheme by Mathur and Murthy(1997) and the central difference scheme by Demirdzic and Muzaferija(1995) have more accurate prediction performance than the other higher-order schemes used in unstructured cell-centered finite volume methods.

• Environmental Engineering Research
• /
• v.23 no.4
• /
• pp.442-448
• /
• 2018

This paper presents the numerical simulation of advection-diffusion mechanism of BOD concentration which was used as an indicator of waste only in one flow-direction of waste stabilization ponds (1-dimension (1-D)). This model was represented in partial differential equation order 2. The purpose of this paper was to determine the simulation of the model 1-D of wastewater transport phenomena based advection-diffusion mechanism and did validate the model. Numerical methods which was used for the solution of this model is finite difference method with Forward Time Central Space scheme. The simulation results which was obtained would be compared with field observation data as a validation model. Collection of field data was carried out in the Wastewater Treatment Plant Sewon, Bantul, D.I. Yogyakarta. The results of numerical simulations were indicate that the advection-diffusion mechanism takes place continuously over time. Then validation of the model was state that there was a difference between the calculation results with the field data, with a correlation value of 0.998.

• Geomechanics and Engineering
• /
• v.18 no.3
• /
• pp.225-234
• /
• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

• 한국방재학회:학술대회논문집
• /
• 2007.02a
• /
• pp.395-398
• /
• 2007

In this study, new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects of the linear Boussinesq equations for the propagation of tsunamis. The new model is applied to near Gadeok island in Pusan about The Central East Sea Tsunami in 1983 and The Hokkaldo Nansei Oki Earthquake Tsunami in 1993 one simulated in the study.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.31 no.6
• /
• pp.331-337
• /
• 2018

This paper presents dynamic algorithm of the MLS(moving least squares) difference method using first order differential Approximation. The governing equations are only discretized by the first order MLS derivative approximation. The system equation consists of an assembly of the approximate function, so the shape of system equation is similar to FEM(finite element method). The CDM(central difference method) is used for time integration of dynamic equilibrium equation. The natural frequency analyses of the MLS difference method and FEM are performed, and two analysis results are compared. Also, the accuracy of the proposed numerical method is verified by displaying the dynamic analysis results together with the results by the existing second order differential approximation. In the process of assembling the first order MLS derivative approximation, the oscillation error was suppressed and the stress distribution was interpreted as relatively uniform.

• Computational Structural Engineering
• /
• v.9 no.3
• /
• pp.187-197
• /
• 1996

An explicit direct time integration method based solution algorithm is presented to predict dynamic buckling response of Euler column. On the basis of large deflection beam theory, a plane frame finite element is formulated and implemented into the solution algorithm. The element formulation takes into account geometrical nonlinearity and overall buckling of steel structural frames. The solution algorithm employs the central difference method. Using the computer program developed by the author, dynamic instability behavior of Euler column under impact loading is investigated by considering the time variation of load, load magnitude, and load duration. The free vibration of Euler column caused by a short duration impact load is also studied. The validity and efficiency of the present formulation and solution algorithm are verified through illustrative numerical examples.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.1827-1832
• /
• 2003

In this research, the simulation method for acoustic sounds by a uniform flow around a two-dimensional circular cylinder by using the finite difference lattice Boltzmann model is explained. To begin with, we examine the boundary condition which determined with the distribution function $f_i^{(0)}$ concerning with density, velocity and internal energy at boundary node. Very small acoustic pressure fluctuation, with same frequency as that of Karman vortex street, is compared with the pressure fluctuation around a circular cylinder. The acoustic sound' propagation velocity shows that acoustic approa ching the upstream, due to the Doppler effect in the uniform flow, slowly propagated. For the do wnstream, on the other hand, it quickly propagates. It is also apparently the size of sound pressure was proportional to the central distance $r^{-1/2}$ of the circular cylinder. The lattice BGK model for compressible fluids is shown to be one of powerful tool for simulation of gas flows.