Two-dimensional Riemann problem for a system of hyperbolic conservation laws
Two-dimensional Riemann problem for a system of hyperbolic conservation laws
- 주제(키워드) Riemann problem , Conservation laws
- 발행기관 고려대학교 대학원
- 지도교수 황운재
- 발행년도 2018
- 학위수여년월 2018. 8
- 유형 Text
- 학위구분 박사
- 학과 대학원 수학과
- 원문페이지 106 p
- 실제URI http://www.dcollection.net/handler/korea/000000081334
- UCI I804:11009-000000081334
- DOI 10.23186/korea.000000081334.11009.0000817
- 본문언어 영어
- 제출원본 000045953840
초록/요약
In this thesis, we consider two-dimensional Riemann problem for 2X2 hyperbolic system with two, three and four constant initial data. We also remove the restriction that each jump of the initial data projects one planar elementary wave. We topologically classify distinct solutions and construct analytical solutions and numerical solutions. The computed numerical solutions clearly con rm the constructed analytic solutions.
more목차
1 Introduction 1
2 Elementary waves 6
2.1 Rarefaction 7
2.2 Contact discontinuity 8
2.3 Shock 9
2.4 Delta shock 10
3 Numerical method 12
4 The Riemann problem with two constant states 15
4.1 Classifi cation of initial data 15
4.2 Construction of the solution 16
5 The Riemann problem with three constant states 23
5.1 Classi fication of initial data 23
5.2 Construction of the solution 25
5.2.1 No delta shock 26
5.2.2 One delta shock 35
5.2.3 Two delta shocks 38
6 The Riemann problem with four constant states 41
6.1 Classi fication of initial data 41
6.2 Construction of the solution 42
6.2.1 No delta shock 43
6.2.2 One delta shock 70
6.2.3 Two delta shocks 82
Bibliography 94
