Description
Taylor & Francis The Two-Dimensional Riemann Problem in Gas Dynamics 1998 Edition by Jiequan Li, Tong. Zhang, Shuli Yang
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. Table of contents: PrefacePreliminariesGeometry of Characteristics and DiscontinuitiesRiemann Solution Geometry of Conservation LawsScalar Conservation LawsOne-Dimensional Scalar Conservation LawsThe Generalized Characteristic Analysis MethodThe Four-Wave Riemann ProblemMach-Reflection-Like Configuration of SolutionsZero-Pressure Gas DynamicsCharacteristics and Bounded DiscontinuitiesSimultaneous Occurrence of Two Blowup MechanismsDelta-Shocks, Generalized Rankine-Hugoniot Relations and Entropy ConditionsThe One-Dimensional Riemann ProblemThe Two-Dimensional Riemann ProblemRiemann Solutions as the Limits of Solutions to Self-Similar Viscous SystemsPressure-Gradient Equations of the Euler SystemThe Pme-Dimensional Riemann ProblemCharacteristics, Discontinuities, Elementary Waves, and ClassificationsThe Existence of Solutions to a Transonic Pressure-Gradient Equation in an Elliptic Region with Degenerate DatumThe Two-Dimensional Riemann Problem and Numerical SolutionsThe Compressible Euler EquationsThe Concepts of Characteristics and DiscontinuitiesPlanar Elementary Waves and ClassificationPSI Approach to Irrotational Isentropic FlowAnalysis of Riemann Solutions and Numerical ResultsTwo-Dimensional Riemann Solutions with AxisymmetryReferencesAuthor Index