On the propagation of a multi-dimensional shock of arbitrary strength
type: Item
instance of: scholarly article
title: On the propagation of a multi-dimensional shock of arbitrary strength
zbMATH Open document ID: 0586.76123
DOI: 10.1007/BF02837254
author: B. George
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
review text: In this paper the kinematics of a curved shock of arbitrary strength has been discussed using the theory of generalized functions. The condition for a nontrivial jump in the flow variables gives the shock manifold equation (SME). An equation for the rate of change of shock strength along the shock rays (defined as the characteristics of the SME) has been obtained. This exact result is then compared with the approximate result of shock dynamics derived by \textit{G. B. Whitham} [e.g.: J. Fluid Mech. 5, 369-386 (1959; Zbl 0085.403)]. In the last section we have derived the conservation form of our shock dynamic equations. These conservation forms would be very useful in numerical computations as it would allow us to derive difference schemes for which it would not be necessary to fit the shock-shock explicitly.
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 3941113
zbMATH Keywords: shock in an ideal gas
zbMATH Keywords: nonlinear waves
zbMATH Keywords: multi-dimensional shock propagation
zbMATH Keywords: curved shock of arbitrary strength
zbMATH Keywords: generalized functions
zbMATH Keywords: nontrivial jump
zbMATH Keywords: shock manifold equation
zbMATH Keywords: change of shock strength
zbMATH Keywords: shock rays
zbMATH Keywords: approximate result of shock dynamics
zbMATH Keywords: conservation form
zbMATH Keywords: difference schemes
MaRDI profile type: Publication
cites work: Q5801144
cites work: Propagation of shock waves in an isentropic, nonviscous gas
cites work: Kinematics of a multi-dimensional shock of arbitrary strength in an ideal gas
cites work: Q5536978
cites work: A new approach to problems of shock dynamics Part I Two-dimensional problems
cites work: A new approach to problems of shock dynamics Part 2. Three-dimensional problems
full work available at URL: https://doi.org/10.1007/bf02837254
OpenAlex ID: W2040573651
description: scientific article; zbMATH DE number 3941113