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REDUCED ORDER SIMULATIONS OF THE BURGERS' EQUATION USING CENTROIDAL VORONOI TESSELLATION
- Author(s)
- 이성환
- Alternative Author(s)
- Lee, SungHwan
- Advisor
- 이형천
- Department
- 일반대학원 이학계열
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2005
- Language
- eng
- Abstract
- Centroidal Voronoi tessellation (CVT)는 연관된 generating point들이 대응하는 Voronoi region들의 무게중심이 되는 성질을 만족하는 주어진 집합의 Voronoi tessellation이다. 이 논문에서, CVT는 시간에 의존하는 버거스 방정식에 대한 reduced-order model을 유도하기 위해 이용된다. 그리고 나서, 그 결과들이 유한요소법 (finite element method)을 이용한 결과들 그리고 proper orthogonal decomposition (POD)를 이용한 결과들과 비교된다.
- Alternative Abstract
- A centroidal Voronoi tessellation (CVT) is a Voronoi Tessellation of a given set such that the associated generating points are centroids (centers of mass) of the corresponding Voronoi regions. In this thesis, CVT is utilized to derive reduced-order models for the time-dependent Burgers equation. Then, CVT-based algorithms are compared with numerical results obtained from finite-element discretization and proper orthogonal decomposition (POD)-based algorithms.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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