• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.49-54
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• 1997

Rice's monotone streamline upwind finite element method, which was proposed to treat convection-dominated flows, is applied to the linear triangular element. An alignment technique of unstructured grids with given velocity fields is used to prevent the interpolation error produced in evaluating the convection term in the upwind method. The alignment of grids is accomplished by optimizing a target function defined with the inner-product of a properly chosen side vector in the element with the velocity field. Two pure advection problems are considered to demonstrate the superiorities of the present approach in solving the convection-dominated flow on the unstructured grid. Solutions obtained with aligned grids are much closer to the exact solutions than those with initial regular grids. The capability of the present approach in predicting the appearance of the secondary vortex in the laminar confined jet impingement is shown by comparing streamlines to those produced by SIMPLE on a highly stretched grid toward the impingement plate.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.141-150
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• 1998

The measurement of strains in stamped sheet metal is essential to the design and manufacture of sound sheet metal products. The measured strains can also be used in verifying the reliability of the computer analysis such as finite element analysis. In most engineering applications, strains are measured from the deformed square grids or deformed circular grids in comparison with the initial undeformed grids. In such a case, however, strains are averaged in each grid and the localized strain in a region smaller than a grid size can not be measured. In the present study, the B-spline surface interpolation technique is introduced in order to measure the strains more exactly and effectively. The strains calculated by using the surface interpolation technique are compared with the strains calculated from the three-noded grids as well as with the finite element analysis.

• Journal of computational fluids engineering
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• v.4 no.2
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• pp.39-46
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• 1999

The FVM(Finite Volume Method) have been used mainly for the flow analyses in the piston-cylinder. The objective of the present study is to analyze numerically the piston-driven intake flows using the FEM(Finite Element Method). The FEM algorithm used in this study is 4-step time-splitting method which requires much less execution time and computer storage than the velocity-pressure integrated method and the penalty method. And the explicit Lax-Wendroff scheme is applied to nonlinear convective term in the momentum equations to prevent checkerboard pressure oscillations. Also, the ALE(arbitrary Lagrangian Eulerian) method is adopted for the moving grids. The calculated results show good agreement in comparison with those by the FVM and the experimental results by the LDA.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.48 no.3
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• pp.200-208
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• 1999

In this paper, the corona discharge is analyzed by Finite Element Method(FEM) combined with Flux-corrected Transport(FCT) algorithm. In the previous papers, Finite Difference Method(FDM) combined with FCT was used. Usually in the FDM, the regionof interest is discretized with structured grids. But to refine local regions with same resolution, much more grids are required for the structured grids than for unstructured grids than for unstructured grids. Therefore, we propose the FEM-FCT method to simulate the corona discharge. The proposed method has good flexibility in model shape and can reduce the computational cost by the local refinement where the physical quantities have steep gradients. Using the proposed method, we study the streamer growth of parallel plate electrodes which is initiated by the low and high perturbation density. We find that the varying the initial density of perturbation has very little effect on the streamer propagation. And the corona discharge of the rod-to-plane electrode is simulated. On the surface of the rod electrode, the high concentration of the electric field gives rise to many number of streamer seeds. The strong axial streamer propagate to the plane electrode. The weaker non-axial streamer repel each other and stop growing more. The results are very similar to those of the papers which used the FDM-FCT method on structured grids. Thus we can conclude that the proposed FEM-FCT method is more efficient than the conventional FDM-FCT method by virtue of the reduction in computational grids number.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.405-416
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• 2005

This study contains the static buckling tests and static buckling analyses for small size grids and full size grids. The buckling tests and finite element analyses were performed to evaluate the buckling characteristics of the spacer grids in a pressurized water reactor fuel assembly and to evaluate the possibility of the prediction lot the buckling strength of spacer grids. The buckling tests were performed for small size grids and full size grids, and the correlations between buckling strength and the number of straps and the correlations between buckling strength and the number of rows are derived based on the test results. The static buckling analyses were performed to identify the effect of the number of rows and the number of columns on the buckling strength of spacer grid by a finite element method using ANSYS program and the results were compared with the buckling test results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.65-92
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• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1103-1119
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• 2007

We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the incompressible problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark problems are given to show the efficiency and effectiveness of the method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.3
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• pp.424-431
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• 2003

The spacer grid is one of the main structural components in the fuel assembly, which supports the fuel rods and maintains coolable geometry from an external load. A vibration test and a finite element analysis using ABAQUS on a dummy fuel rod continuously supported by Optimized H type(OHT) and New Doublet (ND) spacer grids arc performed to obtain the vibration characteristics such as natural frequencies and mode shapes an(1 to verify a finite element model. The results from the test and the finite element analysis are compared by modal assurance criteria (MAC) values. It is resulted that MACs for the first, the third and the fifth mode shapes are relatively good as compared with those of the second an(1 fourth ones. The natural frequency differences between two methods as well as the mode comparison results for the rod with OHT spacer grid are better than those with ND spacer grid. It is judged that the FE model for the ND spacer grid spring should be modified to consider the long contact length which actually happen when the spring supports the rod.

• Steel and Composite Structures
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• v.9 no.3
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• pp.239-253
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• 2009

This paper reviews the concept of tensegrity structures and proposes a new type of dismountable steel tensegrity grids for possible deployment as light-weight roof structures. It covers the fabrication of the prototype structures followed by their instrumentation, destructive testing and numerical analysis. First, a single module, measuring $1m{\times}1m$ in size, is fabricated based on half-cuboctahedron configuration using galvanised iron (GI) pipes as struts and high tensile stranded cables as tensile elements. Detailed instrumentation of the structure is carried out right at the fabrication stage. The structure is thereafter subjected to destructive test during which the strain and the displacement responses are carefully monitored. The structure is modelled and analyzed using finite element method (FEM) and the model generated is updated with the experimental results. The investigations are then extended to a $2{\times}2$ grid, measuring $2m{\times}2m$ in size, fabricated uniquely by the cohesive integration of four single tensegrity modules. After updating and validating on the $2{\times}2$ grid, the finite element model is extended to a $8{\times}8$ grid (consisting of 64 units and measuring $8m{\times}8m$) whose behaviour is studied in detail for various load combinations expected to act on the structure. The results demonstrate that the proposed tensegrity grid structures are not only dismountable but also exhibit satisfactory behaviour from strength and serviceability point of view.