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THE NUMERICAL SOLUTION OF SHALLOW WATER EQUATION BY MOVING MESH METHODS
Suyeon Shin,Woonjae Hwang 충청수학회 2012 충청수학회지 Vol.25 No.3
This paper presents a moving mesh method for solving the hyperbolic conservation laws. Moving mesh method consists of two independent parts: PDE evolution and mesh- redistribution. We compute numerical solution of shallow water equation by using moving mesh methods. In comparison with computations on a ¯xed grid, the moving mesh method appears more accurate resolution of discontinuities.
김동일(Dongil Kim),황운재(Woonjae Hwang),김홍중(Hongjoong Kim),손지영(Jiyoung Son),김정호(Jeongho Kim),이기정(Kijeong Lee),신재현(Jaehyun Shin) 한국HCI학회 2012 한국HCI학회 학술대회 Vol.2012 No.1
본 연구에서는 장애학생 고등교육 환경에서 수학 영역을 중심으로 e-러닝 프로그램을 개발하고 사용성 평가를 실시하여, e-러닝 프로그램 개발의 실제적인 고려사항과 장애학생 평가를 통한 개발 전략의 개선점이 무엇인지를 탐색하고자 하였다. 이에 문헌연구를 통해 장애학생 대상의 e-러닝 설계 전략을 도출하고 수학 미적분학 내용에서 필요한 자료제시 전략을 실제로 구현하여 e-러닝 강좌를 개발하였다. 개발된 프로그램에 대해서는 5 명의 장애학생들이 프로그램 구성과 인터페이스 등에 대해 사용성 평가를 실시하였다. 연구결과, 수식을 디지털화하여 제시하는 특수 언어의 사용, 수식과 그래프의 대체텍스트 제공, 다양한 확대 및 설정 변경 기능, 동기화된 자막 제공 등이 실제적 고려사항으로 나타났다. 장애학생의 사용성 평가 결과, 수식과 그래프의 간결한 제시, 다양한 학습자 조절 기능 제공, 음성정보와 자막의 원활한 연동, 대체텍스트 제공의 보완, 단순한 화면 구성 등이 개선점으로 제시되었다. The purpose of the study is to develop and evaluate an e-learning program for college students with disabilities in the math area. An e-learning module of teaching calculus was developed according to design strategies for students with disabilities. Then, five college students with disabilities(vision, hearing, and mobility disability) evaluated the usability of the e-learning program. The e-learning contents were consisted of learning materials in a variety of formulation, graph, and media to support students with disabilities. The results of the study showed that the practical strategies of e-learning development are digitalizing formulas using MathML, providing alternative text, controlling various functions, and synchronized captions. Additionally, through the results of usability testing a number of solutions to improve the e-learning program were suggested as follows: concisely representing of formulation and graph, multiple controls of size and pace, smooth linkage between voice and captions, alt-text descriptions of most image files, and simple user interface design.
The High Order WENO Scheme on the Adaptive Mesh
Daeki Yoon,Hongjoong Kim,Woonjae Hwang 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5
The paper is concerned with the high order accurate computational method on hyperbolic conservationa law using weighted essentially non-oscillatory (WENO) scheme when nonuniform grids are adaptively introduced near a shock or a contact discontinuity. We apply the WENO scheme on nonuniform spatial grids, and high level of mesh refinement is introduced only in the region where more accurate computation is required such as points of discontinuity or sharp transition layer. The scheme estimates cell averages using the ENO-based interpolation when cells are merged or split. Numerical experiments show that the suggested method preserve the order of the WENO method on the adaptive mesh and that the method can be performed for a sufficiently long time with less computational cost.
Vortex Dynamics of Stratified Shear Flow
Sung-Ik Sohn,Woonjae Hwang 한국산업응용수학회 2006 한국산업응용수학회 학술대회 논문집 Vol.1 No.1
A perturbed interface between fluids of different densities subject to a parallel shear flow is unstable. This interfacial instability is known as the Kelvin-Helmholtz (KH) instability and plays a dominant role in many physical phenomena. The nonlinear evolution of an interface subject to a parallel shear flow is studied on the basis of the vortex sheet model. We perform numerical simulations of the vortex sheet in density stratified fluids by using the point vortex method and investigate various aspects of dynamics of the stratified shear flow.
A TREATMENT OF CONTACT DISCONTINUITY FOR CENTRAL UPWIND SCHEME BY CHANGING FLUX FUNCTIONS
MOUNGIN SHIN,SUYEON SHIN,WOONJAE HWANG 한국산업응용수학회 2013 Journal of the Korean Society for Industrial and A Vol.17 No.1
Central schemes offer a simple and versatile approach for computing approximate solutions of nonlinear systems of hyperbolic conservation laws. However, there are large numerical dissipation in case of contact discontinuity. We study semi-discrete central upwind scheme by changing flux functions to reduce the numerical dissipation and we perform numerical computations for various problems in case of contact discontinuity.
Numerical Simulations of Vortex Sheet Evolution in Stratified Shear Flow
Sohn, Sung-Ik,Hwang, Woonjae Physical Society of Japan 2005 Journal of the Physical Society of Japan Vol.74 No.5
<P>The nonlinear evolution of an interface subject to a parallel shear flow is studied on the basis of the vortex sheet model. We perform numerical simulations of the vortex sheet in density stratified fluids by using the point vortex method. The numerical algorithm based on two types of regularization method improves the stability of the vortex method and provides solutions with much higher resolutions than previous results. The numerical results show that, for a smaller density ratio, the interface has a larger growth rate and a more singular vortex sheet strength and curvature at late times. It is also found that, for an infinite density ratio, the interface has a solution of a travelling wave with no deformations.</P>
Long-time simulations of the Kelvin-Helmholtz instability using an adaptive vortex method.
Sohn, Sung-Ik,Yoon, Daeki,Hwang, Woonjae Published by the American Physical Society through 2010 Physical review. E, Statistical, nonlinear, and so Vol.82 No.4
<P>The nonlinear evolution of an interface subject to a parallel shear flow is studied by the vortex sheet model. We perform long-time computations for the vortex sheet in density-stratified fluids by using the point vortex method and investigate late-time dynamics of the Kelvin-Helmholtz instability. We apply an adaptive point insertion procedure and a high-order shock-capturing scheme to the vortex method to handle the nonuniform distribution of point vortices and enhance the resolution. Our adaptive vortex method successfully simulates chaotically distorted interfaces of the Kelvin-Helmholtz instability with fine resolutions. The numerical results show that the Kelvin-Helmholtz instability evolves a secondary instability at a late time, distorting the internal rollup, and eventually develops to a disordered structure.</P>