• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1752-1756
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• 2008

A simple, accurate and efficient mesh generation technique, the cut-cell method, is able to represent an arbitrarily complex geometry. Both structured and unstructured grid meshes are used in this method. First, the numerical domain is constructed with regular Cartesian grids as a background grid and then the solid boundaries or bodies are cut out of the background Cartesian grids. As a result, some boundary cells can be contained two numerical conditions such as the flow and solid conditions, where the special treatment is needed to simulate such physical characteristics. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. Also, the TVD-WAF method is applied on the Cartesian cut-cell grids to stabilize numerical results. Present method is validated for the rectangular dam break problems. Initially, a conventional grid is constructed with the Cartesian regular mesh only and then applied to the dam-break flow simulation. As a comparative simulation, a cut-cell grids are applied to represent the flow domain rotated with arbitrary angles. Numerical results from this study are compared with the results from the case of the Cartesian regular mesh only. A good agreement is achieved with other numerical results presented in the literature.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.4
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• pp.338-348
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• 2015

In this study, the added resistance of ships in short waves is systematically studied by using two different numerical methods - Rankine panel method and Cartesian grid method – and existing asymptotic and empirical formulae. Analysis of added resistance in short waves has been preconceived as a shortcoming of numerical computation. This study aims to observe such preconception by comparing the computational results, particularly based on two representative three-dimensional methods, and with the existing formulae and experimental data. In the Rankine panel method, a near-field method based on direct pressure integration is adopted. In the Cartesian grid method, the wave-body interaction problem is considered as a multiphase problem, and volume fraction functions are defined in order to identify each phase in a Cartesian grid. The computational results of added resistance in short waves using the two methods are systematically compared with experimental data for several ship models, including S175 containership, KVLCC2 and Series 60 hulls (C_B = 0.7, 0.8). The present study includes the comparison with the established asymptotic and empirical formulae in short waves.

• 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.

• Korean Journal of Computational Design and Engineering
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• v.13 no.6
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• pp.450-458
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• 2008

Recently, Cartesian grid approach has been popular to generate grid meshes for complex geometries in CFD (Computational Fluid Dynamics) because it is based on the non-body-fitted technique. This paper presents a method of an octree generation and boundary cell clipping using section curves for fast octree generation and elimination of redundant intersections between boundary cells and triangles from 3D triangular mesh. The proposed octree generation method uses 2D Scan-Converting line algorithm, and the clipping is done by parameterization of vertices from section curves. Experimental results provide octree generation time as well as Cut-cell clipping time of several models. The result shows that the proposed octree generation is fast and has linear relationship between grid generation time and the number of cut-cells.

• 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.

• 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.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.15-16
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• 2003

An implicit pressure correction method on unstructured Cartesian grid is developed for the incompressible Navier-Stokes equations. An immersed boundary method is also incorporated to treat the body geometry. Tests show that with an appropriate amount of dissipation, the method is second order accurate both in time and space. The driven cavity flows with and without immersed bodies are computed to demonstrate the capability of the present scheme.