• Proceedings of the Korea Water Resources Association Conference
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• 1998.05a
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• pp.259-264
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• 1998

• Journal of Mechanical Science and Technology
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• v.17 no.7
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• pp.986-998
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• 2003

In this paper, an adaptive numerical integration scheme, which does not need non-overlapping and contiguous integration meshes, is proposed for the MLPG (Meshless Local Petrov-Galerkin) method. In the proposed algorithm, the integration points are located between the neighboring nodes to properly consider the irregular nodal distribution, and the nodal points are also included as integration points. For numerical integration without well-defined meshes, the Shepard shape function is adopted to approximate the integrand in the local symmetric weak form, by the values of the integrand at the integration points. This procedure makes it possible to integrate the local symmetric weak form without any integration meshes (non-overlapping and contiguous integration domains). The convergence tests are performed, to investigate the present scheme and several numerical examples are analyzed by using the proposed scheme.

• Journal of Korea Water Resources Association
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• v.34 no.2
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• pp.107-118
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• 2001

This study was to develop a tow-dimensional model system for the hydrodynamic analysis and to apply the system on the downstream of Han River. it is performed to design a GIS-based hydrodynamic system for the scientific shallow water profile analysis, and to compare hydrodraulic modeling is the Petrov-Galerkin's finite element method for flow prediction model. This study was to construct a GIS-based river flow system, and it is useful for supporting user's decision making for the on-line status through various analysis. We expect that the results from this study can be used as one of the guidelines for river analysis and management system in order rivers, reservoirs, and estuaries.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.289-294
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• 2010

Numerical stud of an oscillating body in incompressible fluid is performed. Stabilized finite element method comprising of Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulations of linear triangular elements was employed to solve 2D incompressible Navier-Stokes equations whereas the motion of the body was considered by incorporating the arbitrary Langrangian-Eulerian(ALE) formulation. An algebraic moving mesh strategy is utilized for obtaining body conforming mesh deformation at each time step. Two tests cases, namely motion of a circular cylinder and of an airfoil in incompressible flow were analyzed. The model is first validated against the stationary cases and then the capability to handle moving boundaries is demonstrated.

• Wind and Structures
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• v.27 no.4
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.386-391
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• 2001

A finite element code based on P2P1 tetra element has been developed for the large eddy simulation (LES) of turbulent flows around a complex geometry. Fractional 4-step algorithm is employed to obtain time accurate solution since it is less expensive than the integrated formulation, in which the velocity and pressure fields are solved at the same time. Crank-Nicolson method is used for second order temporal discretization and Galerkin method is adopted for spatial discretization. For very high Reynolds number flows, which would require a formidable number of nodes to resolve the flow field, SUPG (Streamline Upwind Petrov-Galerkin) method is applied to the quadratic interpolation function for velocity variables, Noting that the calculation of intrinsic time scale is very complicated when using SUPG for quadratic tetra element of velocity variables, the present study uses a unique intrinsic time scale proposed by Codina et al. since it makes the present three-dimensional unstructured code much simpler in terms of implementing SUPG. In order to see the effect of numerical diffusion caused by using an upwind scheme (SUPG), those obtained from P2P1 Galerkin method and P2P1 Petrov-Galerkin approach are compared for the flow around a sphere at some Reynolds number. Smagorinsky model is adopted as subgrid scale models in the context of P2P1 finite element method. As a benchmark problem for code validation, turbulent flows around a sphere and a MIRA model have been studied at various Reynolds numbers.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.237-246
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• 1999

A finite element model is studied to simulate unsteady free surface flow based on dynamic wave equation and collocation method. The collocation method is used in conjunction with Hermite polynomials, and resulting matrix equations are solved by skyline method. The model is verified by applying to hydraulic jump, nonlinear disturbance propagation and dam-break flow in a horizontal frictionless channel. The computed results are compared with those by Bubnov-Galerkin and Petrov-Galerkin methods. It is also applied to the North Han River to simulate the floodwave propagation. The computed results have good agreements with those of DWOPER model in terms of discharge hydrographs. The suggested model has proven to be one of the promising scheme for simulating the gradually and rapidly varied unsteady flow in open channels.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.679-698
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• 2020

In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

• Water Engineering Research
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• v.4 no.1
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• pp.45-58
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• 2003

Two-dimensional depth-averaged advection-dispersion equation was simulated using FEM. In the straight rectangular channel, the advection-dispersion processes are simulated so that these results can be compared with analyti-cal solutions for the transverse line injection and the point injection. In the straight domain the standard Galerkin method with the linear basis function is found to be inadequate to the advection-dispersion analysis compared to the upwind finite element scheme. The experimental data in the S-curved channel were compared with the result by the numerical model using SUPG(Streamline upwind Petrov-Galerkin) method.

• Wind and Structures
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• v.14 no.5
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• pp.465-480
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• 2011

In this paper, a stabilized large eddy simulation technique is developed to predict turbulent flow with high Reynolds number. Streamline Upwind Petrov-Galerkin (SUPG) stabilized method and three-step technique are both implemented for the finite element formulation of Smagorinsky sub-grid scale (SGS) model. Temporal discretization is performed using three-step technique with viscous term treated implicitly. And the pressure is computed from Poisson equation derived from the incompressible condition. Then two numerical examples of turbulent flow with high Reynolds number are discussed. One is lid driven flow at Re = $10^5$ in a triangular cavity, the other is turbulent flow past a square cylinder at Re = 22000. Results show that the present technique can effectively suppress the instabilities of turbulent flow caused by traditional FEM and well predict the unsteady flow even with coarse mesh.