• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.46.1-46.1
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• 2019

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.65-78
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• 1999

We present a fast/parallel Poisson solver on disks, based on efficient evaluation of the exact solution given by the Newtonian potential and the Poisson integral. Derived from an integral formula-tion it is more accurate and simpler in parallel implementation and in upgrading to a higher order algorithm than an algorithm which solves the linear system obtained from a differential formulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.8
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• pp.15-25
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• 1997

The integration method of carier concentrations to redcue the discretization error of th box integratio method used in the discretization of the three-dimensional poisson's equation is presented. The carrier concentration is approximated in the closed form as an exponential function of the linearly varying potential in the element. The presented method is implemented in the three-dimensional poisson's equation solver running under the windows 95. The accuracy and the convergence chaacteristics of the three-dimensional poisson's equation solver are compared with those of DAVINCI for the PN junction diode and the n-MOSFET under the thermal equilibrium and the DC reverse bias. The potential distributions of the simulatied devices from the three-dimensional poisson's equation solver, compared with those of DAVINCI, has a relative error within 2.8%. The average number of iterations needed to obtain the solution of the PN junction diode and the n-MOSFET using the presented method are 11.47 and 11.16 while the those of DAVINCI are 21.73 and 23.0 respectively.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.1
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• pp.75-94
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• 2005

Research in the decision sciences has continued to develop a variety of mathematical models as well as software tools supporting corporate decision-making. Yet. in spite of their potential usefulness, the models are little used in real-world decision making since the model solution processes are too complex for ordinary users to get accustomed. This paper proposes an intelligent and flexible model-solver integration framework that enables the user to solve decision problems using multiple models and solvers without having precise knowledge of the model-solution processes. Specifically, for intuitive model-solution, the framework enables a decision support system to suggest the compatible solvers of a model autonomously without direct user intervention and to solve the model by matching the model and solver parameters intelligently without any serious conflicts. Thus, the framework would improve the productivity of institutional model solving tasks by relieving the user from the burden of leaning model and solver semantics requiring considerable time and efforts.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.36-42
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• 2016

One of the obstacles on the grid generation for complex geometries with multi-block structured grids is the domain decomposition. In this paper, the domain decomposition for two-dimensional flow is studied using the flow characteristics. The potential flow equation with the source distribution on the panel surface is solved to extract the information of the flow. The current approach is applied to a two-dimensional cylinder and Bi-NACA0012 problems. The generated grids are applied to generic flow solvers and reasonable results are obtained. It can be concluded that the current methods is useful in the domain decomposition for the multi-block structured grid.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1125-1134
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• 2017

In this paper, we present a new multilevel in space and energy diffusion (MSED) method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1) a grey (one-group) diffusion equation used to efficiently converge the fission source and eigenvalue, (2) a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3) a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

• Journal of Ocean Engineering and Technology
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• v.23 no.4
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• pp.38-46
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• 2009

Two sets of numerical simulations were carried out for a planing hull model ship. In the first, the WAVIS 1.4 linear and nonlinear potential solver was utilized with the free support condition, in which the running posture was determined during calculation. The linear and nonlinear potential calculation results showed qualitative agreement in the trim and resistance coefficient with the MOERI towing tank test. However, the nonlinear potential calculation gave better results than the linear method. In the next simulation, Fluent 6.3.26 with a VOF model and the WAVIS 1.4 nonlinear potential solver were used with the given running posture from the measurement carried out in the MOERI towing tank. Fluent with the VOF method had substantially better agreement with model test results than the results from the WAVIS nonlinear potential calculation for the total resistance coefficient, and for the bow and stern wave patterns, in spite of the much greater computational costs. Both methods can be utilized in planing hull design when their limitations are perceived, and the running posture should be predicted correctly.

• Particle and aerosol research
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• v.9 no.2
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• pp.103-110
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• 2013

The electrostatic precipitator (ESP) has been used for degrading atmospheric pollutants. These devices induce the electrical forces to facilitate the removal of particulate pollutants. The ions travel from the high voltage electrode to the grounded electrode by Coulomb force induced by the electric field when a high voltage is applied between two electrodes. The ions collide with gas molecules and exchange momentum with each other thus inducing fluid motion, electrohydrodynamic (EHD) flow. In this study, for the simulation of electric field and EHD flow in ESPs, an open source EHD solver, "espFoam", has been developed using open source CFD toolbox, OpenFOAM(R) (Open Field Operation and Manipulation). The electric potential distribution and ionic space charge density distribution were obtained with the developed solver, and validated with experimental results in the literature. The comparison results showed good agreement. Turbulence model is also incorporated to simulate turbulent flow; hence the developed solver can analyze laminar and turbulent flow. In distributions of electric potential and space charge, the distributions become distorted and asymmetric as the flow velocity increases. The effect of electrical drift flow was investigated for different flow velocities and the secondary flow in a flow of low velocity is successfully predicted.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.1024-1040
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• 2014

The theoretical background and a numerical solution procedure for a time domain hydroelastic code are presented in this paper. The code combines a VOF-based free surface flow solver with a flexible body motion solver where the body linear elastic deformation is described by a modal superposition of dry mode shapes expressed in a local floating frame of reference. These mode shapes can be obtained from any finite element code. The floating frame undergoes a pseudo rigid-body motion which allows for a large rigid body translation and rotation and fully preserves the coupling with the local structural deformation. The formulation relies on the ability of the flow solver to provide the total fluid action on the body including e.g. the viscous forces, hydrostatic and hydrodynamic forces, slamming forces and the fluid damping. A numerical simulation of a flexible barge is provided and compared to experiments to show that the VOF-based flow solver has this ability and the code has the potential to predict the global hydroelastic responses accurately.