The Two-Dimensional Riemann Problem in Gas Dynamics

NOTE EDITORE

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.

SOMMARIO

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

AUTORE

Li, Jiequan; Zhang, Tong.; Yang, Shuli

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780582244085
• Collana: Monographs and Surveys in Pure and Applied Mathematics
• Dimensioni: 9.75 x 6.75 in Ø 1.61 lb
• Formato: Copertina rigida
• Pagine Arabe: 310