• The Pure and Applied Mathematics
• /
• v.11 no.4
• /
• pp.309-321
• /
• 2004

For a complete open Riemannian manifold, the ideal boundary consists of points at infinity. The so-called Busemann-functions play the role of distance functions for points at infinity. We study the similarity and difference between Busemann-functions and ordinary distance functions.

• Journal of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.87-118
• /
• 1997

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

• Journal for History of Mathematics
• /
• v.16 no.4
• /
• pp.107-115
• /
• 2003

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.12 no.1
• /
• pp.819-831
• /
• 2020

Wind load is one of the major design loads for the hull and mooring of offshore floating structures, especially due to much larger windage area above water than under water. By virtue of extreme design philosophy, fully turbulent flow assumption can be justified and the hydrodynamic characteristics of the flow remain almost constant which implies the wind load is less sensitive to the Reynolds number around the design wind speed than wind profile. In the perspective of meteorology, wind profile used for wind load estimation is a part of Atmospheric Boundary Layer (ABL), especially maritime ABL (MBL) and have been studied how to implement the profile without losing turbulence properties numerically by several researchers. In this study, the MBL is implemented using an open source CFD toolkit, OpenFOAM and extended to unstable ABL as well as neutral ABL referred to as NPD profile. The homogeneity of the wind profile along wind direction is examined, especially with NPD profile. The NPD profile was applied to a semi-submersible rig and estimated wind load was compared with the results from wind tunnel test.

• Nuclear Engineering and Technology
• /
• v.55 no.5
• /
• pp.1911-1923
• /
• 2023

The nuclear safety assessment involving large transient simulations is forcing the community to develop methods for coupling thermal-hydraulics and neutronic codes and three-dimensional (3D) Computational Fluid Dynamics (CFD) codes. In this paper a set of dynamic boundary conditions are implemented in OpenFOAM^Ⓡ in order to apply zero-dimensional (0D) approaches coupling with 3D thermal-hydraulic simulation in a single framework. This boundary conditions are applied to model pipelines, tanks, pumps, and heat exchangers. On a first stage, four tests are perform in order to assess the implementations. The results are compared with experimental data, full 3D CFD, and system code simulations, finding a general good agreement. The semi-implicit implementation nature of these boundary conditions has shown robustness and accuracy for large time steps. Finally, an application case, consisting of a simplified open pool with a cooling external circuit is solved to remark the capability of the tool to simulate thermal hydraulic systems commonly found in nuclear installations.

• Journal of Mechanical Science and Technology
• /
• v.14 no.9
• /
• pp.928-934
• /
• 2000

This paper describes a method developed for the simulation of ring pack lubrication characteristic in an internal combustion engine. In general, the quantity of oil supply for piston ring lubrication may be insufficient in filling the entire volume formed at the interference between the piston ring and the cylinder liner. Thus the oil starvation condition should be considered in analyzing piston ring lubrication. In order to reasonably estimate the amount of oil left over on the cylinder liner, the flow rate at the posterior portion of the interface should be calculated with an adequate boundary condition that confirms flow continuity condition. In this analysis, oil starvation and open-end boundary conditions are considered at the inlet and outlet of the piston rings. The lubrication characteristic of each piston ring is obtained by an iterative method with sequential steps. It is revealed that piston rings are operated under oil starvation in most operating cycles and the result under these conditions are quite different from that with the fully-flooded assumption.

• Proceedings of the KIEE Conference
• /
• 2000.07e
• /
• pp.99-103
• /
• 2000

The finite element method (FEM) is suitable for the analysis of a complicated region that includes nonlinear materials, whereas the boundary element method (BEM) is naturally effective for analyzing a very large region with linear characteristics. Therefore, considering the advantages in both methods, a novel algorithm for the alternate application of the FEM and BEM to magnetic field problems with the open boundary is presented. This approach avoids the disadvantages of the typical numerical methods with the open boundary problem such as a great number of unknown values for the FEM and non-symmetric matrix for the Hybrid FE-BE method. The solution of the overall problems is obtained by iterative calculations accompanied with the new acceleration method.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.10 no.2
• /
• pp.93-99
• /
• 1998

Parabolic approximation and sponge layer are applied as open boundary condition for elliptic finite difference wave model. Generalized conjugate gradient method is used as a solution procedure. Using parabolic approximation a large part of spurious reflection is removed at the spherical shoal experiment and sponge layer boundary condition needs more than 2 wave lengths of sponge layer to give similar results. Simulating the propagation of waves on a rectangular harbor, it is identified that iterative scheme can be applied easily for the non-rectangular computational region.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.5 no.3
• /
• pp.392-403
• /
• 2013

For the analysis of radiating noise problems in medium-to-high frequency ranges, the Energy Flow Boundary Element Method (EFBEM) was developed. EFBEM is the analysis technique that applies the Boundary Element Method (BEM) to Energy Flow Analysis (EFA). The fundamental solutions representing spherical wave property for radiating noise problems in open field and considering the free surface effect in underwater are developed. Also the directivity factor is developed to express wave's directivity patterns in medium-to-high frequency ranges. Indirect EFBEM by using fundamental solutions and fictitious source was applied to open field and underwater noise problems successfully. Through numerical applications, the acoustic energy density distributions due to vibration of a simple plate model and a sphere model were compared with those of commercial code, and the comparison showed good agreement in the level and pattern of the energy density distributions.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.33 no.2
• /
• pp.94-103
• /
• 1991

This study was carried out to investigate the engineering characteristics of the R.C circular ring sector plate with various boundary conditions and then to propose a rational and paraical method for application of finite element method to R.C structures. The stiffness matrix of the circular ring sector plate was obtained by using the multi-base coordinate system in which the base-coordinate systems were constructed for each nodal point of the quadrilateral element in order to reflect the complicated boundary conditions conveniently and correctly. The R.C element stiffness matrix was constructed by adding the stiffness coefficients of the steel-bar element into the plate bending element stiffness matrix. Herein, the steel-bar element was treated as the common beam element. Using the above method, the effects of steel-bar can be considered without increasing of the numbers of element and nodal points.