• 호남수학학술지
• /
• 제35권3호
• /
• pp.373-379
• /
• 2013

In contrast with numerous identities involving the binomial coefficients and the Stirling numbers of the first and second kinds, a few identities involving the Eulerian numbers have been known. The objective of this note is to present certain interesting and (presumably) new identities involving the Eulerian numbers by mainly making use of Worpitzky's identity.

• 충청수학회지
• /
• 제26권3호
• /
• pp.591-599
• /
• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• 충청수학회지
• /
• 제26권1호
• /
• pp.191-196
• /
• 2013

In this paper we derive some identities on Eulerian polynomials of higher order from non-linear ordinary differential equations. We show that the generating functions of Eulerian polynomials are solutions of our non-linear ordinary differential equations.

• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.443-450
• /
• 2016

In this paper we give some properties, explicit formulas, several identities, a connection with tangent numbers and polynomials, and some integral formulas.

• 대한수학회보
• /
• 제36권1호
• /
• pp.47-61
• /
• 1999

In this paper we difine poly-Euler numbers which generalize ordinary Euler numbers. We construct a p-adic poly-Euler measure by the poly-Euler polynomials and derive an integral formula.

• 한국지하수토양환경학회지:지하수토양환경
• /
• 제11권1호
• /
• pp.37-44
• /
• 2006

본 연구는 오염물 거동에 대한 수치해석을 위해 보편적으로 사용되고 있는 수치 방법들의 장단점을 총괄적으로 나타내고, 효율적인 수치모델링 기법 개발을 위해 ELLAM과 LEZOOMPC를 비교분석하였다. 지하수 분야에서 가장 많이 사용되는 수치 방법은 Eulerian-Lagrangian 방식과 Eulerian 방식인데, Eulerian-Lagrangian 방식은 수치영역 내에서 일반적으로 질량을 보존하지 못하고, 경계조건을 체계적으로 처리하지 못하는 한계를 갖고 있다. 반면에 Eulerian 빙식은 시간 및 공간 절삭 오차로 인해서 시간 간격 및 격자 크기를 극히 줄여야 하는 제약을 갖고 있다. 최근 10 년간 지하수 분야에서 크게 대두되고 있는 수치기법인 ELLAM(Eulerian Lagrangian Localized Adjoint Method)은 Eulerian-Lagrangian 방식과 Eulerian 방식에서 나타나는 수치 제약점이나 한계점을 동시에 해결하는 수치기법으로 알려져 왔다. 그러나 본 연구에서는 ELLAM의 장단점을 파악하고 보완점을 제안한다. ELLAM의 단점을 파악하기 위해, mesh Peclet number가 다른 예제들을 설정하고, 그 예제들에 대한 ELLAM, LEZOOMPC(Lagrangian-Eulerian ZOOMing Peak and valley Capturing)와 visual MODFLOW의 수치결과들을 해석해와 비교하였다. Mesh Peclet number가 무한대일 때 ELLAM의 수치결과는 수치진동으로 인해 해석해와 일치하지 않았으나, LEZOOMPC의 수치 결과는 해석해와 일치했다. 위의 결과는 ELLAM의 수치오차가 LEZOOMPC의 특성을 이용하여 개선 및 보완될 수 있는 가능성을 시사해 준다. 따라서 ELLAM에 LEZOOMPC의 후향 입지추적, 전향 입지추적, 선택적 국부 격자 세립화 과정과 최고/최저 농도점 이동 추적 과정을 결합하면 ELLAM의 수치적 장점을 유지하면서 mesh Peclet number에 제약을 받지 않는 효율적인 수치모델링 기법을 개발할 수 있을 것으로 판단된다.

• East Asian mathematical journal
• /
• 제10권2호
• /
• pp.329-337
• /
• 1994

• 대한기계학회논문집B
• /
• 제23권1호
• /
• pp.43-57
• /
• 1999

The fluid flow and heat transfer in a thin liquid film are investigated numerically. The flow Is assumed to be two-dimensional laminar and surface tension is considered. The most important characteristics of this flow is the existence of a hydraulic jump through which the flow undergoes very sharp and discontinuous change. Arbitrary Lagrangian-Eulerian(ALE) method is used to describe moving free boundary and a modified SIMPLE algorithm based on streamline upwind Petrov-Galerkin(SUPG) finite element method is used for time marching iterative solution. The numerical results obtained by solving unsteady full Navier-Stokes equations are presented for planar and radial flows subject to constant wall temperature or constant wall heat flux, and compared with available experimental data. It Is discussed systematically how the inlet Reynolds and Froude numbers and surface tension affect the formation of a hydraulic jump. In particular, the effect of temperature dependent fluid properties is also discussed.

• Nuclear Engineering and Technology
• /
• 제55권10호
• /
• pp.3754-3767
• /
• 2023

Turbulent jet discharges in subcooled water pools are essential for safety systems in nuclear power plants, specifically in the pressure suppression pool of boiling water reactors and In-containment Refueling Water Storage Tank of advanced pressurized water reactors. The gas and liquid flow in these systems is investigated using multiphase flow analysis. This field has been extensively examined using a combination of experiments, theoretical models, and Computational Fluid Dynamics (CFD) simulations. ANSYS CFX offers two approaches to model multiphase flow behavior. The non-homogeneous Eulerian-Eulerian Model has been used in this work; it computes global information and is more convenient to study interpenetrated fluids. This study utilized the Large Eddy Simulation Model as the turbulence model, as it is better suited for non-stationary and buoyant flows. The CFD results of this study were validated with experimental data and theoretical results previously obtained. The figures of merit dimensionless penetration length and the dimensionless buoyancy length show good agreement with the experimental measurements. Correlations for these variables were obtained as a function of dimensionless numbers to give generality using only initial boundary conditions. CFD numerical model developed in this research has the capability to simulate the behavior of non-condensable gases discharged in water.

• Wind and Structures
• /
• 제16권5호
• /
• pp.411-431
• /
• 2013

A computational study of vortex-induced transverse vibrations of a cylinder with low mass-damping is presented. An Arbitrary Lagrangian-Eulerian (ALE) formulation of the Unsteady Reynolds-Averaged Navier-Stokes equations (URANS), along with the Spalart-Allmaras (SA) one-equation turbulence model, are coupled conservatively with rigid body motion equations of the cylinder mounted on elastic supports in order to study the amplitude and frequency response of a freely vibrating cylinder, its flow-induced motion, Vortex Street, near-wake flow structure, and unsteady loading in a moderate range of Reynolds numbers. The time accurate response of the cylinder from rest to its limit cycle is studied to explore the effects of Reynolds number on the start of large displacements, motion amplitude, and frequency. The computational results are compared with published physical experiments and numerical studies. The maximum amplitudes of displacements computed for various Reynolds numbers are smaller than the experimental values; however, the overall agreement of the results is quite satisfactory, and the upper branch of the limit-cycle displacement amplitude vs. reduced velocity response is captured, a feature that was missed by other studies. Vortex shedding modes, lock-in phenomena, frequency response, and phase angles are also in agreement with experiments.