• Geomechanics and Engineering
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• v.18 no.6
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• pp.651-659
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• 2019

The IB-SEM numerical method combines the spectral/hp element method and the rigid immersed boundary method. This method avoids the problems of low computational efficiency and errors that are caused by the re-division of the grid when the solids move. Based on the Fourier transformation and the 3D immersed boundary method, the 3D IB-SEM system was established. Then, using the open MPI and the Hamilton HPC service, the computational efficiency was increased substantially. The flows around a cylinder and a sphere were simulated by the system. The surface of the cylinder generates vortices with alternating shedding, and these vortices result in a periodic force acting on the surface of the cylinder. When the shedding vortices enter the flow field behind the cylinder, a recirculation zone is formed. Finally, the three-dimensional pore flow was successfully investigated.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.1
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• pp.22-37
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• 2016

This article investigates numerical modeling of surface piercing propeller (SPP) in unsteady open water condition using boundary element method. The home code based on BEM has been developed for the prediction of propeller performance, unsteady ventilation pattern and cross flow effect on partially submerged propellers. To achieve accurate results and correct behavior extraction of the ventilation zone, finely mesh has generated around the propeller and especially in the situation intersection of propeller with the free surface. Hydrodynamic coefficients and ventilation pattern on key blade of SPP are calculated in the different advance coefficients. The values obtained from this numerical simulation are plotted and the results are compared with experiments data and ventilation observations. The predicted ventilated open water performances of the SPP as well as ventilation pattern are in good agreement with experimental data. Finally, the results of the BEM code/experiment comparisons are discussed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.457-464
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• 2001

The aeroacoustic phenomena in the simple rectangular open cavity are well published by many researchers. But the geometry shapes of aircraft landing gear wells, weapon bays, etc. are more complicate than that of the simple retangular cavity. They are more similar to the cavity having cover-plates at adges, or Helmholtz resonator. Therefore, the effects of cover-plates existing on edges of rectangular open cavity are numerically investigated in this paper. The compressible Navier-Stokes equations are solved for two-dimensional cavities with laminar boundary layers upstream. The high-order and high-resolution numerical schemes are used for the evaluation of spatial derivatives and the time integration. Physically correct numerical boundary conditions and buffer zone techniques are implemented to produce time-accurate solutions in the whole computation domain. The computational domain is large enough to directly resolve a portion of the radiated acoustic field. Results show that the cover-plates existing on edges of cavity reduce the noise convected from cavity, make the frequency of noise become higher, and change the directivity pattern. So these results can be used in the design of a low noise cavity.

• Water for future
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• v.20 no.3
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• pp.219-228
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• 1987

Shallow water equations were applied to the flow in and through the opening to a coastal bay with different open boundary conditions. The open boundaries, shaped like a semi-circle, have various radii. the open boundaries therefore are defined in terms of radius given by multiple of the opening width, 2B. It was found from numerical experiments that for adequate results proper radius of the boundary is 3B or greater and that for radius greater than 3B the solutions become stable. For the solution of the shallow water equations a typical Galerkin's finite element method was used.

• 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.

• Water for future
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• v.22 no.3
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• pp.315-322
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• 1989

The effects of open boundary conditions including the radiation condition are compared by utilizing the $L^{2_}$-norm and RMS error in the numerical modeling of ocean problem. In numerical tests of $M_2$ tide, grid size and bed roughness are considered and analyzed. For the $M_2$ tide test in a simplified bay where the analytical solutions are available, it is found that improved radiating boundary condition(IMPSOM) may increase the reliability of computed results by 40% of $L^{2_}$-norm and 96% of RMS error than the open boundary condition without radiation effect. In case of using the half-size grids, better results are obtained. It is also found that the IMPSOM is applicable with satisfaction when the bottom friction is included.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.451-460
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• 2009

We consider the existence of solutions of a nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=f(x, u)$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. We obtain two new results by linking theorem.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.6
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• pp.1-10
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• 1997

By using the boundary element method, the cahracterization and the circuit modelling of the coplanar waveguide (CPW) discontinuities are performed bvia quasi-static approximation. The capacitive equivalent circuits are obtained by developing the 3-D boundary element method with collocation method. On the triangular patch, the numerical scheme employed the linear basis functions and the analytic solutions of the integrals on the singular points. The capacitive discontinuities of gaps, end-gaps, and open-ends are characterized and the results compared with the conductor backed coplanar waveguides.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.851-863
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• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• East Asian mathematical journal
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• v.39 no.1
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• pp.29-36
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• 2023

In this paper, we consider φ-Laplacian nonlocal boundary value problems with singular weight function which may not be in L¹(0, 1). The existence and nonexistence of positive solutions to the given problem for parameter λ belonging to some open intervals are shown. Our approach is based on the fixed point index theory.