• Journal of Korea Foundry Society
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• v.29 no.1
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• pp.33-37
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• 2009

Cartesian grid system has mainly been used in the casting simulation even though it does not nicely represent sloped and curved surfaces. These distorted boundaries cause several problems. A special treatment is necessary to clear these problems. In this paper, we propose a new method that can consider the cutting cells which are cut by casting and mold based on the partial cell treatment (PCT). This method provides a better representation of geometry surface and will be used in the computation of velocities that are defined on the cell boundaries in the Cartesian grid system. Various test examples for several casting process were computed and validated. The analysis results of more accurate fluid flow pattern and less momentum loss owing to the stepped boundaries in the Cartesian grid system were confirmed. By using the cut cell method, performance of computation gets better because of reducing the whole number of meshes.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.518-522
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• 2011

Cartesian grid system has mainly been used in the casting simulation even though it does not nicely represent sloped and curved surfaces. These distorted boundaries cause several problems. A special treatment is necessary to clear these problems. A cut cell method on Cartesian grids has been developed to simulate three-dimensional mold filling Cut cells at a cast-mold interface are generated on Cartesian grids. Governing equations were computed using volume and areas of cast at cut cells. In this paper, we propose a new method that can consider the cutting cells which are cut by casting and mold based on the patial cell treatment (PCT). This method provides a better representation of geometry surface and will be used in the computation of velocities that are defined on the cell boundaries in the Cartesian gird system. Various test examples for several casting process were computed and validated. The analysis results of more accurate fluid flow pattern and less momentum loss owing to the stepped boundaries in the Cartesian grid system were confirmed. We can know the momentum energy at the cut cell is conserved by using the cut cell method. By using the cut cell method. performance of computation gets better because of reducing the whole number of meshes.

• Journal of the Society of Naval Architects of Korea
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• v.50 no.2
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• pp.79-87
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• 2013

In this paper, an Euler equation solver based on a Cartesian-grid method and non-uniform staggered grid system is applied to predict the ship motion response and added resistance in waves. Water, air, and solid domains are identified by a volume-fraction function for each phase and in each cell. For capturing the interface between air and water, the tangent of hyperbola for interface capturing (THINC) scheme is used with a weighed line interface calculation (WLIC) method. The volume fraction of solid body embedded in a Cartesian-grid system is calculated by a level-set based algorithm, and the body boundary condition is imposed by volume weighted formula. Added resistance is calculated by direct pressure integration on the ship surface. Numerical simulations for a Wigley III hull and an S175 containership in regular waves have been carried out to validate the newly developed code, and the ship motion responses and added resistances are compared with experimental data. For S175 containership, grid convergence test has been conducted to investigate the sensitivity of grid spacing on the motion responses and added resistances.

• 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.

• Journal of the Society of Naval Architects of Korea
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• v.56 no.4
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• pp.308-315
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• 2019

In this study, numerical simulations of slamming impact pressure acting on the flat plate and wedge type models using the cartesian-grid system and Modified Marker-Density Method (MMD method) were performed and the results were examined. The flat plate and wedge type models were selected as target objects, the turbulence characteristics were considered by applying the Sub-Grid Scale (SGS) turbulence model. Through this study, how the pressure acting on the target objects according to the incident angle influences the slamming impact pressure was examined and the results were compared with the flow characteristics of other experimental results. Also, the degree of slamming impact pressure is evaluated with respect to the cartesian-grid system and MMD method, which is easy to use and has a high degree of calculation for free surface.

• Journal of Korea Foundry Society
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• v.43 no.6
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• pp.302-309
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• 2023

In general, castings often have complex shapes and significant variations in thickness within a single product, making grid generation for simulations challenging. Casting flows involve multiphase flows, requiring the tracking of the boundary between air and molten metal. Additionally, considerable time is spent calculating pressure fields due to density differences in a numerical analysis. For these reasons, the Cartesian grid system has traditionally been used in mold filling simulations. However, orthogonal grids fail to represent shapes accurately, leading to a momentum loss caused by the stair-like grid patterns on curved and sloped surfaces. This can alter the flow of molten metals and result in incorrect casting process designs. To address this issue, simulations in the Cartesian grid system involve creating a large number of grids to represent shapes more accurately. Alternatively, the Cut Cell method can be applied to address the problems arising from the Cartesian grid system. In this study, analysis results based on the number of grid in the Cartesian grid system for a casting flow analysis were compared with results obtained using the Cut Cell method. Casting flow simulations of actual products during various casting processes were also conducted, and these results were analyzed with and without applying the Cut Cell method.

• Journal of computational fluids engineering
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• v.16 no.1
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• pp.73-82
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• 2011

In this paper, the vortex-induced vibration of circular cylinders is studied using the immersed boundary method on the Cartesian mesh. The Reynolds numbers considered is from 100 to 200. Using the configuration of tendemly arranged multiple circular cylinders, the vortex shedding behind of the cylinders and their flow-induced motion are investigated. The staggered MAC grid arrangement, which is the typical grid system for the incompressible flow on the Cartesian meshes, is utilized. Pressure correction method is applied for solving the divergence-free incompressible velocity field. The body motion is described by immersed boundary technique that has advantages for moving object on the fixed computational domain. It is also discussed for the computational noise in hydrodynamic forces when body motion is represented by the immersed boundary method. The Predictor/Corrector method is used for simulating the nonlinear response of the elastically mounted cylinder excited by vortex-shedding.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.3
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• pp.253-258
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• 2012

The Cartesian grid system has generally been used in casting simulations, even though it does not represent sloped and curved surfaces very well. These distorted boundaries cause several problems, and special treatment is necessary to resolve them. A cut cell method on a Cartesian grid has been developed for the simulation of threedimensional mold filling. Cut cells at a cast/mold interface are generated on Cartesian grids, and the governing equations are computed using the volume and areas of the cast at the cut cells. In this paper, we propose a new method based on the partial cell treatment (PCT) that can consider the cutting cells which are cut by the cast and the mold. This method provides a better representation of the surface geometry, and will be used in the computation of velocities that are defined on the cell boundaries in the Cartesian gird system. Various test examples for several casting process are computed and validated.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1500-1508
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• 2001

This paper represents the importance of dependent variables in non-orthogonal curvilinear coordinates just as the importance of those variables of convective scheme and turbulence model in computational fluid dynamics. Each of Cartesian, physical covariant and physical contravariant velocity components was tested as the dependent variables of momentum equations in the staggered grid system. In the flow past a circular cylinder, the results were computed to use each of three variables and compared to experimental data. In the skewed driven cavity flow, the results were computed to check the grid dependency of the variables. The results used in Cartesian and physical contravariant components of velocity in cylinder flow show the nearly same accuracy. In the case of Cartesian and contravariant component, the same number of vortex was predicted in the skewed driven cavity flow. Vortex strength of Cartesian component case has about 30% lower value than that of the other two cases.

• Journal of the Society of Naval Architects of Korea
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• v.48 no.3
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• pp.260-266
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• 2011

For long slender offshore structures, such as cables and pipe lines, their interaction with surrounding fluid flow becomes an important issue for global design of ocean systems. We employ a long circular cylinder as a representative case of slender offshore structure. A flexibly mounted cylinder in cross-flow generates complex vortex shedding and results in oscillation of the structure. In this paper, flow behind a circular cylinder at Re=100 is simulated. The vortex shedding pattern and flow induced motion are examined in the cross flow configuration as well as with various yaw-angled configurations. The "Lock-in" phenomenon is also observed when reduced velocity is approximately 4.0. The MAC Grid system, which is the typical grid system for Cartesian mesh and pressure correction methods, are used for solving the incompressible Navier-Stokes equations. Predictor/Corrector method is applied for obtaining a non-linear response of structure at the flexibly mounted. The existance and motion of the body is represented by the immersed boundary technique.