• 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 Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1890-1899
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• 1992

In bonded structures, there are V-notched cracks in dissimilar materials and the stress concentration of these V-notched cracks causes to occur interface cracks in dissimilar materials Therefore the strength evaluation of V-notched cracks in dissimliar materials seems to be important. The stress fields of a V-notched cracks is known as .sigma.$_{ij}$ .var. K $r_{p-1}$,where K is the stress intensity factor and p-1 is the stress singularity. When the distance, r, approaches to 0 at the stress fields of V-notched cracks, the stresses become infinites by two more stress singularities of p-1 and p-1 is no more -0.5. Stress singularities and stress intensity factors for V-notched cracks in dissimilar materials are treated and discussed. The Newton-Raphson method which is an efficient numerical method for solving a non-linear equation is used for solving stress sigularities. And stress intensity factors are solved by the collocation method using the Newton-Raphson and least squares method. The effects of stress intensity factors and stress singularities on stress fields of V-notched cracks in dissimilar materials are studied by using photoelasic isochromatic frings patterns obtained from computer graphics.s.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.14 no.2
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• pp.127-139
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• 1996

This paper presents a procedure to recover sea surface heights (SSH) and free-air (FA) gravity anomalies from dense satellite altimeter SSH data with enhanced accuracies over the full spectrum of the gravity field. A wavenumber correlation filtering (WCF) of co-linear SSH tracks is developed for the coherent signals of sub-surface geological masses. Orbital cross-over adjustments with bias parameters are applied to the filtered SSH data, which are then separated into two groups of ascending and descending tracks and gridded with tensioned splines. A directional sensitive filter (DSF) is developed to reduce residual errors in the orbital adjustments that appear as track patterned SSH. Finally, FA gravity anomalies can be obtained by the application of a gradient filter on a high resolution estimate of geoid undulations after subtracting dynamic sea surface topography (DSST) from the SSH. These procedures are applied to the Geosat Geodetic Mission (GM) data of the southern oceans in a test area of ca. $900km\;\times{1,200}\;km$ to resolve geoid undulations and FA gravity anomalies to wavelengths of-10 km and larger. Comparisons with gravity data from ship surveys, predictions by least squares collocation (LSC), and 2 versions of NOAA's predictions using vertical deflections illustrate the performance of this procedure for recovering all elements of the gravity spectrum. Statistics on differences between precise ship data and predicted FA gravity anomalies show a mean of 0.1 mgal, an RMS of 3.5 mgal, maximum differences of 10. 2 mgal and -18.6 mgal, and a correlation coefficient of 0.993 over four straight ship tracks of ca. 1,600 km where gravity changes over 150 mgals.