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Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach’s experiment for the compressible Euler system, i. e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

Acta Mathematicae Applicatae Sinica , Volume 22 (2) – Jan 1, 2006

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-006-0296-5
Publisher site
See Article on Publisher Site

Abstract

We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach’s experiment for the compressible Euler system, i. e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2006

References