• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Steel and Composite Structures
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• v.49 no.3
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• pp.281-291
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• 2023

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

• The Journal of the Acoustical Society of Korea
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• v.25 no.1E
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• pp.32-35
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• 2006

The screech tone of underexpanded jet is numerically calculated without any specific modeling for the screech tone itself. Fourth-order optimized compact scheme and fourth-order Runge-Kutta method are used to solve the 2D axisymmetric Euler equation. Adaptive nonlinear artificial dissipation model and generalized characteristic boundary condition are also used. The screech tone, generated by a closed loop between instability waves and quasi-periodic shock cells at the near field, is reasonably analyzed with present numerical methods for the underexpanded jet having Mach number 1.13. First of all, the centerline mean pressure distribution is calculated and compared with experimental and other numerical results. The instantaneous density contour plot shows Mach waves due to mixing layer convecting supersonically, which propagate downstream. The pressure signal and its Fourier transform at upstream and downstream shows the directivity pattern of screech tone very clearly. Most of all, we can simulate the axisymmetric mode change of screech tone very precisely with present method. It can be concluded that the basic phenomenon of screech tone including the frequency can be calculated by using high-order and high-resolution schemes without any specific numerical modeling for screech tone feedback loop.

• Journal of the Korean Society of Combustion
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• v.13 no.1
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• pp.17-22
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• 2008

A partly implicit/quasi-explicit method is introduced for the solution of detailed chemical kinetics with stiff source terms based on the standard fourth-order Runge-Kutta scheme. Present method solves implicitly only the stiff reaction rate equations, whereas the others explicitly. The stiff equations are selected based on the survey of the chemical Jaconian matrix and its Eigenvalues. As an application of the present method constant pressure combustion was analyzed by a detailed mechanism of hydrogen-air combustion with NOx chemistry. The sensitivity analysis reveals that only the 4 species in NOx chemistry has strong stiffness and should be solved implicitly among the 13 species. The implicit solution of the 4 species successfully predicts the entire process with same accuracy and efficiency at half the price.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.797-811
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• 2015

An analytical-computational method along with finite element analysis (FEA) has been employed to analyse the dynamic behaviour of deteriorated structures excited by time- varying mass. The present analysis is focused on the comparative study of a double cracked beam with inclined edge cracks and transverse open cracks subjected to traversing mass. The assumed computational method applied is the fourth order Runge-Kutta method. The analysis of the structure has been carried out at constant transit mass and speed. The response of the structure is determined at different crack depth and crack inclination angles. The influence of the parameters like crack depth and crack inclination angles are investigated on the dynamic behaviour of the structure. The results obtained from the assumed computational method are compared with those of the FEA for validation and found good agreements with FEA.

• Wind and Structures
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• v.23 no.5
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• pp.421-447
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• 2016

Wind-induced and earthquake-induced excitations on tall structures can be effectively controlled by Tuned Liquid Damper (TLD). This work presents a numerical simulation procedure to study the performance of tuned liquid tank- structure system through ${\sigma}$-transformation based fluid-structure coupled solver. For this, a 'C' based computational code is developed. Structural equations are coupled with fluid equations in order to achieve the transfer of sloshing forces to structure for damping. Structural equations are solved by fourth order Runge-Kutta method while fluid equations are solved using finite difference based sigma transformed algorithm. Code is validated with previously published results. The minimum displacement of structure is observed when the resonance condition of the coupled system is satisfied through proper tuning of TLD. Since real-time excitations are random in nature, the performance study of TLD under random excitation is also carried out in which the Bretschneider spectrum is used to generate the random input wave.

• Journal of Institute of Convergence Technology
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• v.1 no.1
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• pp.41-47
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• 2011

With the world-wide demand on the emission minimization, the needs on the diesel aftertreatment devices with high efficiency are also increasing. In order to effectively develop or design a high-performance diesel particulate filter, a clear understanding on the deposition and regeneration mechanism is required. In the present study, a theory on the lumped parameter model for wall-flow type diesel particulate filters is described focusing on the deposition efficiency, pressure drop inside the filter. The fourth order explicit Runge-Kutta method is utilized for the mass flow rate computation. Engine operation modes with controlled and uncontrolled regeneration options are selected. The computational lumped parameter model is validated by comparing the computed results with the measured data.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.3
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• pp.166-177
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• 2005

This study developed the jet integral model to analyze the behavior of the wastewater discharge in the near field using the fourth order Runge-Kutta method in order to numerically solve the problems of six ordinary differential equations and six unknowns. This jet integral model used the entrainment hypothesis and the manipulation of sonle shape constant. This study also conducted the hydraulic experiments fnr single horizontal buoyant Jet using LIF through the calibration procedure. The results calculated by the previous models, CORMIX 1 and VISJET, and the proposed jet integral model were compared to the hydraulic experimental results. The centerline trajectories predicted by the proposed model were in good agreements with the experimental results in the transition region whereas the trajectories calculated by the VISJET model agreed well with the measured data in the momentum and buoyancy-dominated regions. The centerline dilution calculated by the proposed model agreed generally with the measured dilution in the intial and transition regions while the centerline dilution predicted by the CORMIX 1 was in good agreements with the experimental results in the momentum and buoyancy-dominated regions.

• Advances in aircraft and spacecraft science
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• v.5 no.2
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• pp.251-258
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• 2018

This work illustrates the progress of a TAS activity at exploring the challenges and the benefits of the Virtual Shaker Testing (VST) approach. The definition and the validation of new computational methodologies with respect to the state of the art were encouraged throughout this activity. The shaker Finite Element (FE) model in lateral configuration was built for the purpose and it was merged with the SpaceCraft (S/C) FE model, together with the S/C-Shaker adapter. FE matrices were reduced through the Craig-Bampton method. The VST transient analysis was performed in MATLAB(R) numerical computing environment. The closed-loop vibration control is accounted for and the solution is obtained through the fourth-order Runge Kutta method. The use of pre-existing built-in functions was limited by authors with the aim of tracing the impact of all the problems' parameters in the solution. Assumptions and limitations of the proposed methodology are detailed throughout this paper. Some preliminary results pertaining to the current progress of the activity are thus illustrated before the conclusions.

• The KSFM Journal of Fluid Machinery
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• v.11 no.4
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• pp.14-21
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• 2008

The prediction for gaseous leak flows through a narrow crack is important for a leak-before-break (LBB) analysis. Therefore, the methodology to obtain the flow characteristics of gaseous leak flow in a narrow crack for the wide range by using the product of friction factor and Reynolds number correlations (fRe) for a micro-channel is developed and presented. The correlation applied here was proposed by the previous study. The fourth-order Runge-Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure and the regular-Falsi method was also employed to find the inlet Mach number. A narrow crack whose opening displacement ranges from 10 to $100{\mu}m$ with a crack length in the range from 2 to 200mm was chosen for sample prediction. The present results are compared with both numerical simulation results and available experimental measurements. The results are in excellent agreement with them. The leak flow rate can be approximately predicted by using proposed methodology.