• Journal of Mechanical Science and Technology
• /
• v.14 no.1
• /
• pp.84-92
• /
• 2000

A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.267-277
• /
• 2011

This paper is concerned with eigenvalues of second-order vector equations on time scales with boundary value conditions. Properties of eigenvalues and matrix-valued solutions are studied. Relationships between eigenvalues of different boundary value problems are discussed.

• Journal of applied mathematics & informatics
• /
• v.39 no.3_4
• /
• pp.295-302
• /
• 2021

In this paper, we propose a new iterative algorithm to automatically prove the existence of solutions for a unilateral boundary value problems for second order equations.

• Proceedings of the KSME Conference
• /
• 2001.06e
• /
• pp.404-409
• /
• 2001

An account of second-order fractional-step methods and boundary conditions for the incompressible Navier-Stokes equations is presented. The present work has aimed at (i) identification and analysis of all possible splitting methods of second-order splitting accuracy; and (ii) determination of consistent boundary conditions that yield second-order accurate solutions. It has been found that only three types (D, P and M) of splitting methods called the canonical methods are non-degenerate so that all other second-order splitting schemes are either degenerate or equivalent to them. Investigation of the properties of the canonical methods indicates that a method of type D is recommended for computations in which the zero divergence is preferred, while a method of type P is better suited to the cases when highly-accurate pressure is more desirable. The consistent boundary conditions on the tentative velocity and pressure have been determined by a procedure that consists of approximation of the split equations and the boundary limit of the result. The pressure boundary condition is independent of the type of fractional-step methods. The consistent boundary conditions on the tentative velocity were determined in terms of the natural boundary condition and derivatives of quantities available at the current timestep (to be evaluated by extrapolation). Second-order fractional-step methods that admit the zero pressure-gradient boundary condition have been derived. The boundary condition on the new tentative velocity becomes greatly simplified due to improved accuracy built in the transformation.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.823-833
• /
• 2000

In this paper, we develop the method of quasilinearization comvined with the methos of upper and lower solutions for singular second order boundary value problems in weighted spaces. The sequences constructed converge uniformly and monotonically to the unique of the second singular order boundary value problem. Further we prove the rate of convergence is quadratic.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1123-1148
• /
• 2016

The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.

• The Bulletin of The Korean Astronomical Society
• /
• v.44 no.1
• /
• pp.46.1-46.1
• /
• 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 Powder Materials
• /
• v.27 no.4
• /
• pp.339-342
• /
• 2020

Since the interaction between the second-phase particle and grain boundary was theoretically explained by Zener and Smith in the late 1940s, the interaction of the second-phase particle and grain boundary on the microstructure is commonly referred to as Zener pinning. It is known as one of the main mechanisms that can retard grain growth during heat treatment of metallic and ceramic polycrystalline systems. Computer simulation techniques have been applied to the study of microstructure changes since the 1980s, and accordingly, the second-phase particle-grain boundary interaction has been simulated by various simulation techniques, and further diverse developments have been made for more realistic and accurate simulations. In this study, we explore the existing development patterns and discuss future possible development directions.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.16 no.3
• /
• pp.35-47
• /
• 1979

Wave resistance of a parabolic thin ship, with its boundary layer and wake taken into account, was calculated up to second order. In addition to the double-model source distribution on the centerplane, image sources of the wave potential were calculated to keep the body introduced boundary condition undisturbed. Boundary layer and wake effects on the wave-making resistance were included by generating an irrotational flow which matches that exterior to the boundary layer and wake. For this purpose, the boundary layer and wake were calculated. The wave resistance refined with second-order corrections are found to be very important for wave resistance calculations even at moderate Froude numbers($Fr=0.2{\sim}0.3$). Wave-potential corrections are dominate around the bow. On the other hand, Viscosity plays and important role at the stern with its boundary layer and wake development.

• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.651-660
• /
• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.