• Journal of Positioning, Navigation, and Timing
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• v.11 no.4
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• pp.297-304
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• 2022

The models used for ionosphere error correction in positioning using Global Navigation Satellite System (GNSS) are representatively Klobuchar model and NeQuick model. Although these models can correct the ionosphere error in real time, the disadvantage is that the accuracy is only 50-60%. In this study, a method for polynomial modeling of Global Ionosphere Map (GIM) which provides Vertical Total Electron Content (VTEC) in grid type was studied. In consideration of Ionosphere Pierce Points (IPP) of satellites with a receivable elevation angle of 15 degrees or higher on the Korean Peninsula, the target area for model generation and provision was selected, and the VTEC at 88 GIM grid points was modeled as a polynomial. The developed VTEC polynomial model shows a data reduction rate of 72.7% compared to GIM regardless of the number of visible satellites, and a data reduction rate of more than 90% compared to the Slant Total Electron Content (STEC) polynomial model when there are more than 10 visible satellites. This VTEC polynomial model has a maximum absolute error of 2.4 Total Electron Content Unit (TECU) and a maximum relative error of 9.9% with the actual GIM. Therefore, it is expected that the amount of data can be drastically reduced by providing the predicted GIM or real-time grid type VTEC model as the parameters of the polynomial model.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.25 no.6_2
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• pp.645-651
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• 2007

In general, contours in digital vector maps, which represent terrain characteristics and shape, are created by 3D digitizing the same height points using aerial photographs on the analytical or digital plotters with stereoscopic viewing. Hence, it requires lots of task, and subjective decision and experience of the operators. DTMs are generated indirectly by using contours since the national digital maps do not include digital terrain model (DTM) data. In this study, model key points which depict the important information about terrain characteristics were extracted from the contours. Further, determination of the efficient and flexible grid sizes were proposed to generate optimal DTM in terms of both quantitative and qualitative aspects. For this purpose, a progressive sampling technique was implemented, i.e., the smaller grid sizes are assigned for the mountainous areas where have large relief while the larger grid sizes are assigned for the relatively flat areas. In consequence, DTMs with multi-grid for difference areas could be generated instead of DTMs with a fixed grid size. The multi-grid DTMs reduce computations for data processing and provide fast display.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.39-47
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• 2000

A great deal of computing time and a large computer memory are needed to solve wave equation in a large complex subsurface layers using the finite difference method. The computing time and memory can be reduced by decreasing the number of grid points per minimum wave length. However, the decrease of grids may cause numerical dispersion and poor accuracy. In this study we performed the grid dispersion analysis for several rotated finite difference operators, which was commonly used to reduce grids per wavelength with accuracy in order to determine the solution for the acoustic wave equation in frequency domain. The rotated finite difference operators were to be extended to 81, 121 and 169 difference stars and studied whether the minimum grids could be reduced to 2 or not. To obtain accuracy (numerical errors less than $1\%$) the following was required: more than 13 grids for conventional 5 point difference stars, 9 grids for 9 difference stars, 3 grids for 25 difference stars, and 2.7 grids for 49 difference stars. After grid dispersion analysis for the new rotated finite difference operators, more than 2.5 grids for 81 difference stars, 2.3 grids for 121 difference stars and 2.1 grids for 169 difference stars were needed. However, in the 169 difference stars, there was no solution because of oscillation of the dispersion curves in the group velocity curves. This indicated that the grids couldn't be reduced to 2 in the frequency acoustic wave equation. According to grid dispersion analysis for the determination of grid points, the more rotated finite difference operators, the fewer grid points. However, the more rotated finite difference operators that are used, the more complex the difference equation terms.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.2
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• pp.206-218
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• 2014

The wave attenuation by floating breakwaters in high amplitude waves, which can lead to wave overtopping and breaking, is examined by numerical simulations. The governing equations, the Navier-Stokes equations and the continuity equation, are calculated in a fixed Cartesian grid system. The body boundaries are defined by the line segment connecting the points where the grid line and body surface meet. No-slip and divergence free conditions are satisfied at the body boundary cell. The nonlinear waves near the moving body is defined using the modified marker-density method. To verify the present numerical method, vortex induced vibration on an elastically mounted cylinder and free roll decay are numerically simulated and the results are compared with those reported in the literature. Using the present numerical method, the wave attenuations by three kinds of floating breakwaters are simulated numerically in a regular wave to compare the performance.

• Ocean Systems Engineering
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• v.7 no.3
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• pp.195-223
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• 2017

This paper presents 3D numerical simulations of a Free Standing Hybrid Riser under Vortex Induced Vibration, with prescribed motion on the top to replace the motion of the buoyancy can. The model is calculated using a fully implicit discretization scheme. The flow field around the riser is computed by solving the Navier-Stokes equations numerically. The fluid domain is discretized using the overset grid approach. Grid points in near-wall regions of riser are of high resolution, while far field flow is in relatively coarse grid. Fluid-structure interaction is accomplished by communication between fluid solver and riser motion solver. Simulation is based on previous experimental data. Two cases are studied with different current speeds, where the motion of the buoyancy can is approximated to a 'banana' shape. A fully three-dimensional CFD approach for VIV simulation for a top side moving Riser has been presented. This paper also presents a simulation of a riser connected to a platform under harmonic regular waves.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.3
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• pp.277-300
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• 2016

The motion of a floating body and the free surface flow are the most important design considerations for ships and offshore platforms. In the present research, a numerical method is developed to simulate the motion of a floating body and the free surface using a fixed rectilinear grid system. The governing equations are the continuity equation and Naviere-Stokes equations. The boundary of a moving body is defined by the interaction points of the body surface and the centerline of a grid. To simulate the free surface the Modified Marker-Density method is implemented. Ships advancing in regular waves, the interaction of waves by a fixed circular cylinder array and the response amplitude operators of an offshore platform are simulated and the results are compared with published research data to check the applicability. The numerical method developed in this research gives results good enough for application to the initial design stage.

• Water Engineering Research
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• v.1 no.3
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• pp.187-197
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• 2000

This paper describes an adaptive quadtree-based 2DH wave-current interaction model which is able to predict wave breaking, shoaling, refraction, diffraction, wave-current interaction, set-up and set-down, mixing processes (turbulent diffusion), bottom frictional effects, and movement of the land-water interface at the shoreline. The wave period-and depth-averaged governing equations are discretised explictly by means of an Adams-Bashforth second-order finite difference technaique on adaptive hierarchical staggered quadtree grids. Grid adaptation is achieved through seeding points distributed according to flow criteria(e.g. local current gradients). Results are presented for nearshore circulation at a sinusoidal beach. Enrichment permits refined modelling of important localised flow features.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.331-349
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• 2006

The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.4.2-4
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• 2003

In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.

• Journal of the Korean Society of Safety
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• v.17 no.1
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• pp.99-104
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• 2002

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration for circular curved beams including mid-surface extension and the effects of rotatory inertia. Fundamental frequencies are calculated for the members with various end conditions and opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.