• Advances in aircraft and spacecraft science
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• v.7 no.3
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• pp.215-228
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• 2020

As is shown in the paper, the Koltunov-Rzhanitsyn singular kernel of heredity (when constructing mathematical models of the dynamics problem of the hereditary theory of viscoelasticity) adequately describes real mechanical processes, best approximates experimental data for a long period of time. A mathematical model of the problem of the flutter of viscoelastic plates moving in a gas with a high supersonic velocity is given. Using the Bubnov-Galerkin method, discrete models of the problem of the flatter of viscoelastic plates flowed over by supersonic gas flow are obtained. A numerical method is developed to solve nonlinear integro-differential equations (IDE) for the problem of the hereditary theory of viscoelasticity with weakly singular kernels. A general computational algorithm and a system of application programs have been developed, which allow one to investigate the nonlinear dynamic problems of the hereditary theory of viscoelasticity with weakly singular kernels. On the basis of the proposed numerical method and algorithm, nonlinear problems of the flutter of viscoelastic plates flowed over in a gas flow at an arbitrary angle are investigated. In a wide range of changes in various parameters of the plate, the critical velocity of the flutter is determined. It is shown that the singularity parameter α affects not only the oscillations of viscoelastic systems, but the critical velocity of the flutter as well.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.2
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• pp.47-54
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• 1987

Linear and nonlinear hydrodynamic force, which acts on submerged circular and eilliptic cylinders in oscillations as well as in advancing motion, are investigated as an initial-boundary value problem using a numerical method, which makes use of the source distribution on the body surface and the spectral method for treating the free surface waves. In the numerical code developed here, the boundary condition at the body surface is linearized. Using the numerical code so attained, nonlinear effects for different forward speeds and of the large-amplitude motion are computed. One of the major findings is that, when the forward speed is large, the added mass has its minimum and the damping force change rapidly around the frequency corresponding to the speed-frequency parameter, $\tau$=0.25, Compared to the result of Grue's [10], who used linear theory to get abrupt changes in values of the added mass and the damping force at the frequency corresponding to $\tau$=0.25, the present study, which takes nonlinear effects into account, shows much smoother variations near the frequency.

• Wind and Structures
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• v.34 no.1
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• pp.91-100
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• 2022

Numerical simulations are conducted to investigate the uniform flow (UF) and sinusoidal streamwise flow (SSF) over an oscillating 5:1 rectangular cylinder with harmonic heaving motion at initial angles of attack of α = 0° and 3° using two-dimensional, unsteady Reynolds-averaged Navier-Stokes (URANS) equations. First, the aerodynamic parameters of a stationary 5:1 rectangular cylinder in UF are compared with the previous experimental and numerical data to validate the capability of the computationally efficient two-dimensional URANS simulations. Then, the unsteady flow field and aerodynamic forces of the oscillating 5:1 rectangular cylinder in SSF are analysed and compared with those in UF to explore the effect of SSF on the rectangular cylinder. Results show that the alternative vortex shedding is disturbed by SSF both at α = 0° and 3°, resulting in a considerable decrease in the vortex-induced force, whereas the unsteady lift component induced by cylinder motion remains almost unchanged in the SSF comparing with that in UF. Notably, the strong buffeting forces are observed at α = 3° and the energy associated with unsteady lift is primarily because of the oscillations of SSF. In addition, the components of unsteady lift induced by the coupling effects of SSF and cylinder motion are discussed in detail.

• Geomechanics and Engineering
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• v.2 no.2
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• pp.141-156
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• 2010

In the framework of meshfree methods, a new methodology is developed based on radial point interpolation method (RPIM). This methodology is applied to a one-dimensional contaminant transport modelling in the saturated porous media. The one-dimensional form of advection-dispersion equation involving reactive contaminant is considered in the analysis. The Galerkin weak form of the governing equation is formulated using 1D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Numerical examples representing various phenomena, which occur during migration of contaminants, are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the analytical and finite element solutions. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. In order to test the practical applicability and performance of the RPIM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.

• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.123-132
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• 2001

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-deformable beams with a high length over thickness ratio. Based upon Timoshenko's theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the field of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. However in the numerical process to integrate strain energy, the second derivative of the standard Moving Least Square (MLS) shape functions must be evaluated, thus requiring at least a $C^1$ continuity of MLS shape functions instead of $C^0$ continuity in the conventional EFGM. Yet this hindrance is overcome effortlessly by only using at least a $C^1$ weight function. One-dimensional quartic spline weight function with $C^2$ continuity is therefore adopted for this purpose. Various numerical results in this work indicate that the modified version of the EFGM does not exhibit transverse shear locking, reduces stress oscillations, produces fast convergence, and provides a surprisingly high degree of accuracy even with coarse domain discretizations.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.52-61
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• 2014

The present paper deals with the efficient computation of higher-order CFD methods for compressible flow using graphics processing units (GPU). The higher-order CFD methods, such as discontinuous Galerkin (DG) methods and correction procedure via reconstruction (CPR) methods, can realize arbitrary higher-order accuracy with compact stencil on unstructured mesh. However, they require much more computational costs compared to the widely used finite volume methods (FVM). Graphics processing unit, consisting of hundreds or thousands small cores, is apt to massive parallel computations of compressible flow based on the higher-order CFD methods and can reduce computational time greatly. Higher-order multi-dimensional limiting process (MLP) is applied for the robust control of numerical oscillations around shock discontinuity and implemented efficiently on GPU. The program is written and optimized in CUDA library offered from NVIDIA. The whole algorithms are implemented to guarantee accurate and efficient computations for parallel programming on shared-memory model of GPU. The extensive numerical experiments validates that the GPU successfully accelerates computing compressible flow using higher-order method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.1
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• pp.131-141
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• 1994

Three characteristics-based split-operator methods were applied to a longitudinal pollutant dispersion problem, and the results were compared with those of several Eulerian schemes. The split-operator methods consisted of generalized upwind, two-point fourth-order and sixth-order Holly-Preissmann schemes, respectively, for the advection calculation, and the Crank-Nicholson scheme for the diffusion calculation. Compared with the Eulerian schemes tested, split-operator methods using the Holly-Preissmann schemes gave much more accurate computational results. Eulerian schemes using centered difference approximations for the advection term resulted in numerical oscillations, and those using backward difference resulted in numerical diffusion, both of which were more severe for smaller value of the longitudinal dispersion coefficient.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.11
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• pp.948-956
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• 2012

This paper presents the computations of the longitudinal and directional stability derivatives for the SDM(Standard Dynamic Model). The static and dynamic derivatives are evaluated at once using forced harmonic oscillations in the pitch and yaw directions. For the numerical simulations, a 3-D Euler solver that uses a dual time stepping method for unsteady time accurate simulations is applied. This work investigates the variation of the derivatives in terms of the Mach number and the several motion parameters. Good agreement of the pitch and yaw stability derivatives with previously published numerical results and experimental results are observed.

• Structural Engineering and Mechanics
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• v.46 no.5
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• pp.713-734
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• 2013

Bridges are vital components of the railroads. High speed of travel, the periodic and oscillatory nature of the loads and the comparable vehicle bridge weight ratio distinguish the railway bridges from the road bridges. The close proximity between estimations by some numerical methods and the measured data for the bridge-vehicle dynamic response under the moving load conditions has boosted the confidence in the numerical analyses. However, there is hardly any report regarding the responses of the railway bridges under the effect of the trains entering from the opposite directions while running at unequal speed and having dissimilar geometries. It is the purpose of this article to present an analytical method for the dynamic analysis of the railway bridges under the influence of two opposing series of moving loads. The bridge structural damping and many modes of vibrations are included. The concept of modal superposition is used to solve for the system motion equations. The method of solution is indeed a computer assisted analytical solution. It solves for the system motion equations and gives output in terms of the bridge deflection. Some case studies are also considered for the validation of the proposed method. Furthermore, the effects of varying some parameters such as the distance between the bogies, and the bogie wheelset distance are studied. Also, the conditions of resonance and cancellation in the dynamic response for a variety of vehicle-bridge specifications are investigated.

• Journal of computational fluids engineering
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• v.17 no.3
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• pp.99-107
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• 2012

In this paper, the shock waves in compressible solids and liquids are simulated using a six-equation diffuse interface multiphase flow model that is extended to the Cochran and Chan equation of state. A pressure relaxation method based on a volume fraction function and a pressure-correction equation are newly implemented to the six-equation model. The developed code has been validated by a shock tube problem with liquid nitromethane and an impact problem of a copper plate on a solid explosive. In addition, a new problem, an impact of a copper plate on liquid nitromethane, has been solved. The present code well shows the wave structures in compressible solids and liquids without any numerical oscillations and overshoots. After the impact of a solid copper plate on liquid, two shock waves (one propagates into liquid and the other into solid) are generated and a material interface moves to the impacting direction. The computational results show that the shock velocity inside the liquid linearly increases with the impact velocity.