论文摘要
本文主要研究了Euler方程组的Riemann问题的解中的波与波的连接分析和几何性质,研究了波线的单调性、凹凸性等性质。并在考虑气体燃烧后,分析Euler方程组Riemann的问题的波与波的连接状态以及几何性质。本文主要安排如下。第一章主要介绍了相关的守恒律方程组的Riemann问题的研究历史和发展现状以及本文的研究内容。第二章主要介绍了守恒系统方程组的Riemann问题等与本文相关的知识。第三章介绍了非等熵气体Euler方程组Riemann问题的混合波情况,根据Rankine-Hugoniot条件以及激波的Lax条件等研究连接左右状态的混合波的情况以及性质。特别地,我们给出了在给定左右状态下,Riemann问题的存在由激波、切触间断、稀疏波构成的各种形式的解的充要条件。第四章研究了含燃烧的非等熵气体Euler方程组Riemann问题,根据Rankine-Hugoniot条件得出了压强与密度的关系即H曲线。对含燃烧的非等熵气体Euler方程组Riemann问题产生激波解和稀疏波解的情况进行了分析。
论文目录
文章来源
类型: 硕士论文
作者: 瞿霞
导师: 戴文荣
关键词: 方程组,问题,条件,激波,切触间断,稀疏波,激波的条件,气体燃烧,曲线
来源: 上海师范大学
年度: 2019
分类: 基础科学
专业: 力学
单位: 上海师范大学
分类号: O35
总页数: 48
文件大小: 1678K
下载量: 68
相关论文文献
- [1].Mapping of Least ρ-Dirichlet Energy between Doubly Connected Riemann Surfaces[J]. Acta Mathematica Sinica 2020(06)
- [2].The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section[J]. Chinese Annals of Mathematics,Series B 2020(04)
- [3].Riemann函数性质及实数完备性的推导[J]. 科技经济市场 2019(07)
- [4].Riemann–Hilbert-type Boundary Value Problems on a Half Hexagon[J]. Acta Mathematica Sinica 2017(09)
- [5].Generalized Riemann problem for Euler system Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday[J]. Science China(Mathematics) 2017(04)
- [6].Inverse Scattering Transform of the Coupled Sasa–Satsuma Equation by Riemann–Hilbert Approach[J]. Communications in Theoretical Physics 2017(05)
- [7].非齐次非对称Keyfitz-Kranzer气体方程组的Riemann问题[J]. 四川师范大学学报(自然科学版) 2020(06)
- [8].Multi-Soliton Solutions for the Coupled Fokas–Lenells System via Riemann–Hilbert Approach[J]. Chinese Physics Letters 2018(07)
- [9].Perturbed Riemann Problem for a Scalar Chapman-Jouguet Combustion Model[J]. Chinese Annals of Mathematics(Series B) 2015(02)
- [10].Automorphism Groups of Pseudo-real Riemann Surfaces of Low Genus[J]. Acta Mathematica Sinica 2014(01)
- [11].Riemann映射与单连通区域分类[J]. 中国科学:数学 2013(03)
- [12].Riemann boundary value problems and reflection of shock for the Chaplygin gas[J]. Science China(Mathematics) 2012(04)
- [13].THE VANISHING PRESSURE LIMIT OF SOLUTIONS TO THE SIMPLIFIED EULER EQUATIONS FOR ISENTROPIC FLUIDS[J]. Annals of Differential Equations 2012(01)
- [14].Riemann-Stieltjes可积的充要条件[J]. 北京师范大学学报(自然科学版) 2011(02)
- [15].ON MNTS FORMULA[J]. Acta Mathematica Scientia 2010(01)
- [16].Two-Dimensional Riemann Problems for the Compressible Euler System[J]. Chinese Annals of Mathematics 2009(06)
- [17].广义解析函数的广义Riemann-Hilbert问题[J]. 华东理工大学学报(自然科学版) 2009(06)
- [18].Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary:Shocks and Contact Discontinuities[J]. Communications in Theoretical Physics 2008(11)
- [19].An application of the Riemann-Roch theorem[J]. Science in China(Series A:Mathematics) 2008(04)
- [20].Multiple Positive Solutions to Singular Fractional Differential System with Riemann-Stieltjes Integral Boundary Condition[J]. Communications in Mathematical Research 2019(03)
- [21].关于向量值函数Riemann积分的若干研究[J]. 云南大学学报(自然科学版) 2019(05)
- [22].A Riemann-Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line[J]. Acta Mathematicae Applicatae Sinica 2018(03)
- [23].A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line[J]. Chinese Annals of Mathematics(Series B) 2016(03)
- [24].二维实系数线性双曲型方程组角域上的Riemann问题（英文）[J]. 应用数学与计算数学学报 2015(03)
- [25].Riemann-Hilbert Problem and Its Well-Posed-Ness for Elliptic Complex Equations of First Order in Multiply Connected Domains[J]. Journal of Mathematical Research with Applications 2014(04)
- [26].关于Riemann可积理论的教学探讨[J]. 高等数学研究 2012(06)
- [27].半平面中一类Riemann-Hilbert边值逆问题[J]. 贵州师范大学学报(自然科学版) 2011(01)
- [28].Riemann-Stieltjes可积函数的本质[J]. 西华大学学报(自然科学版) 2009(06)
- [29].保角变换法解无穷曲线上的Riemann边值问题[J]. 宁夏师范学院学报 2009(06)
- [30].Remarks on Thurston's Construction of Pseudo-Anosov Maps of Riemann Surfaces[J]. Chinese Annals of Mathematics 2008(01)
标签：方程组论文; 问题论文; 条件论文; 激波论文; 切触间断论文; 稀疏波论文; 激波的条件论文; 气体燃烧论文; 曲线论文;