Mathematical Analysis of Shock Wave Reflection

ISBN-13: 9789811577543 / Angielski / Miękka / 2021 / 264 str.

Shuxing Chen

Opis

This book is aimed to make careful analysis to various mathematical problems derived from shock reflection by using the theory of partial differential equations. The occurrence, propagation and reflection of shock waves are important phenomena in fluid dynamics. Comparing the plenty of studies of physical experiments and numerical simulations on this subject, this book makes main efforts to develop the related theory of mathematical analysis, which is rather incomplete so far.  

 

The book first introduces some basic knowledge on the system of compressible flow and shock waves, then presents the concept of shock polar and its properties, particularly the properties of the shock polar for potential flow equation, which are first systematically presented and proved in this book. Mathematical analysis of regular reflection and Mach reflection in steady and unsteady flow are the most essential parts of this book. To give challenges in future research, some long-standing open problems are listed in the end.

 

This book is attractive to researchers in the fields of partial differential equations, system of conservation laws, fluid dynamics, and shock theory. 

Spis treści

1.Introduction

  1.1 Physical Background of Shock Reflection

  1.2 Equations and Boundary Conditions

  1.3 Reflection of Plane Shock

2. Shock Polar Analysis

  2.1 Shock Polar for Euler Equation

  2.2 Shock Polar for Potential Flow Equation

  2.3 Regular Reflection and Mach Configuration

3. Perturbation of Regular Shock Reflection

  3.1 Regular Reflection Containing Supersonic Shock in Two-Dimensional Space

  3.2 Regular Reflection Containing Supersonic Shock in Three-Dimensional Space

4. Stability of Structure of Mach Reflection

  4.1 Reduction and Classification of Mach Configuration

  4.2 Lagrange Transformation and Canonical Form of Nonlinear System

  4.3 Estimates of Linearized Problem Derived from E-E Type Mach Configuration

  4.4 Convergence of Iterative Process and Stability of E-E Type Mach Configuration

  4.5 Stability of E-H Type Mach Configuration

5.  Shock Reflection in Unsteady Flow

  5.1 Shock Reflection by a Smooth Surface

  5.2 Regular Reflection of Plane Shock by a Ramp

  5.3 Mach Reflection of Plane Shock by a Ramp

6.  Problems for Further Consideration

  6.1 Discussion on Full Euler System

  6.2 Reflection in Three-Dimensional Space

  6.3 Big Disturbance and Global Solution

  6.4 Transmission of Different Configuration of Shock Reflection

Appendix

O autorze

Shuxing Chen, is a Full Professor of Fudan University since 1984. He has been Academician of Chinese Academy of Sciences since 2013. He was awarded National Natural Science Award twice in 1982 and 2005. His main research field is theory and applications of partial differential equations.