• Proceedings of the KSME Conference
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• 2000.04b
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• pp.282-289
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• 2000

Direct numerical solution for flow and heat transfer for Benard convection with a body is obtained using an accurate and efficient Fourier-Chebyshev collocation and multi-domain method. The flow and temperature fields are obtained fur different Rayleigh numbers and thermal boundary conditions of body. The body has adiabatic and constant temperature conditions. The existence of a body gives different flow and heat transfer fields in the system, compared to pure Benard convection. The flow and temperature fields are also affected by the thermal boundary condition of a body.

• Journal of computational fluids engineering
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• v.14 no.4
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• pp.93-100
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved successively in the moving least square sense. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as a FVM.

• Journal of the Korean GEO-environmental Society
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• v.10 no.6
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• pp.135-141
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• 2009

Fracturing technique using fluid injection into the borehole is widely used technology in the industry for the geothermal heat, oil, and gas extraction. Dealing with fluid-driven natural fractures such as dike and vein indirectly, design technology would be improved by adapting their principles. In this paper, mechanical interaction between the segments is evaluated by modeling highly segmented and closely spaced fluid-driven natural fractures. The number of segments is 71 with 3,339 measured apertures in which the interaction is considerably predicted. To evaluate mechanical interaction, boundary collocation method is used and the net pressure is calculated by using least square method to fit measured apertures. As a result, in case that mechanical interaction is considered, two pressures as fitting parameters are sufficient to capture measured apertures.

• Journal of the Korean GEO-environmental Society
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• v.10 no.4
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• pp.65-71
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• 2009

Hydraulic fracturing technology has been widely applied in the industry for the recovery of the natural resources such as gas, oil and geothermal heat from hot dry rock. During hydraulic fracturing stimulation, multiple cracks are created resulting in mechanical interaction between cracks. Such an interaction influences obtaining hydraulic fracturing key parameters (crack opening, length, and borehole net pressure). The boundary collocation method (BCM) has been proved to be very effective in considering mechanical interaction. However, for better confidence, it needs to be verified by comparison with analytical solutions such as stress intensity factors. In this paper, three cases, single fracture in remote uniaxial tension, single fracture in remote shear stress field and two arbitrary segments in an infinite plane loaded at infinity are considered. As a result, the BCM is proved to be valid technique to consider mechanical interaction between cracks and can be used to estimate the hydraulic fracturing parameters such as opening of the fracture, and so on.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.34 no.10
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• pp.379-383
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• 1985

A method employing infinite elements is described for the magnetic field computations of the magnetic circuits with permanent magnet. The system stiffness matrix is derived by a variational approach, while the interfacial boundary conditions between the finite element regions and the infinite element regions are dealt with using collocation method. The proposed method is applied to a simple linear problems, and the numerical results are compared with those of the standard finite element method and the analytic solutions. It is observed that the proposed method gives more accurate results than those of the standard finite element method under the same computing efforts.

• Journal of Information Processing Systems
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• v.19 no.5
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• pp.563-575
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• 2023

Trajectory planning is a key technology for unmanned aerial vehicles (UAVs) to achieve complex flight missions. In this paper, a terminal constraints conversion-based Gauss pseudospectral trajectory planning optimization method is proposed. Firstly, the UAV trajectory planning mathematical model is established with considering the boundary conditions and dynamic constraints of UAV. Then, a terminal constraint handling strategy is presented to tackle terminal constraints by introducing new penalty parameters so as to improve the performance index. Combined with Gauss-Legendre collocation discretization, the improved Gauss pseudospectral method is given in detail. Finally, simulation tests are carried out on a four-quadrotor UAV model with different terminal constraints to verify the performance of the proposed method. Test studies indicate that the proposed method performances well in handling complex terminal constraints and the improvements are efficient to obtain better performance indexes when compared with the traditional Gauss pseudospectral method.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.239-244
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved by successively in the moving least square sense. Some weighing functions were tested in order to investigate the up-winding effect for the convection term. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as FVM.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1291-1310
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• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.737-748
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• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• Structural Engineering and Mechanics
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• v.69 no.6
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• pp.667-676
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• 2019

Minimizing the stress concentration around hypotrochoid hole in finite metallic plates under in-plane loading is an important consideration in engineering design. In the analysis of finite metallic plate, the effective factors on stress distribution around holes include curvature radius of the corner of the hole, hole orientation, plate's aspect ratio, and hole size. This paper aims to investigate the impact of these factors on stress analysis of finite metallic plate with central hypotrochoid hole. To obtain the lowest value of stress around a hypotrochoid hole, a swarm intelligence optimization method named ant lion optimizer is used. In this study, with the hypothesis of plane stress circumstances, analytical solution of Muskhelishvili's complex variable method and conformal mapping is employed. The plate is taken into account to be finite, isotropic and linearly elastic. By applying suitable boundary conditions and least square boundary collocation technique, undefined coefficients of stress function are found. The results revealed that by choosing the above-mentioned factor correctly, the lowest value of stress would be obtained around the hole allowing to an increment in load-bearing capacity of the structure.