The two-dimensional Riemann problem in gas dynamics
著者
書誌事項
The two-dimensional Riemann problem in gas dynamics
(Pitman monographs and surveys in pure and applied mathematics, 98)
Longman, 1998
大学図書館所蔵 全28件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. [289]-298) and index
内容説明・目次
内容説明
The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians.
This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function.
The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.
目次
Preface
Preliminaries
Geometry of Characteristics and Discontinuities
Riemann Solution Geometry of Conservation Laws
Scalar Conservation Laws
One-Dimensional Scalar Conservation Laws
The Generalized Characteristic Analysis Method
The Four-Wave Riemann Problem
Mach-Reflection-Like Configuration of Solutions
Zero-Pressure Gas Dynamics
Characteristics and Bounded Discontinuities
Simultaneous Occurrence of Two Blowup Mechanisms
Delta-Shocks, Generalized Rankine-Hugoniot Relations and Entropy Conditions
The One-Dimensional Riemann Problem
The Two-Dimensional Riemann Problem
Riemann Solutions as the Limits of Solutions to Self-Similar Viscous Systems
Pressure-Gradient Equations of the Euler System
The Pme-Dimensional Riemann Problem
Characteristics, Discontinuities, Elementary Waves, and Classifications
The Existence of Solutions to a Transonic Pressure-Gradient Equation in an Elliptic Region with Degenerate Datum
The Two-Dimensional Riemann Problem and Numerical Solutions
The Compressible Euler Equations
The Concepts of Characteristics and Discontinuities
Planar Elementary Waves and Classification
PSI Approach to Irrotational Isentropic Flow
Analysis of Riemann Solutions and Numerical Results
Two-Dimensional Riemann Solutions with Axisymmetry
References
Author Index
「Nielsen BookData」 より