On methods of calculating successive positions of a shock front
type: Item
instance of: scholarly article
title: On methods of calculating successive positions of a shock front
zbMATH Open document ID: 0659.76074
DOI: 10.1007/BF01194343
author: S. H. Smith
published in: Acta Mechanica
publication date: 1988-01-01T00:00:00Z
review text: We have discussed limits of the validity of Whitham's characteristic rule for finding successive positions of a shock in one space dimension. We start with an example for which the exact solution is known and show that the characteristic rule gives correct result only if the state behind the shock is uniform. Then we take the gas dynamic equations in two cases: one of a shock propagating through a stratified layer and other down a nonuniform tube and derive exact equations for the evolution of the shock amplitude along a shock path. These exact results are then compared with the results obtained by the characteristic rule. The characteristic rule not only incorrectly accounts for the deviation of the state behind the shock from a uniform state but also gives a coefficient in the equation which differ significantly from the exact coefficients for a wide range of values of the shock strength.
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 4079044
zbMATH Keywords: successive positions of a shock front
zbMATH Keywords: exact solution
MaRDI profile type: Publication
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: Q3720161
cites work: On the propagation of a multi-dimensional shock of arbitrary strength
cites work: Q4151274
Recommended article: Q5284542
Recommended article: Q4512093
Recommended article: Q4830255
Recommended article: Methods of shock wave calculation
Recommended article: Q3848055
Recommended article: Q3178376
Recommended article: A Method for the Numerical Calculation of Hydrodynamic Shocks
Recommended article: Q3330806
Recommended article: A Method for Shock Calculation
Recommended article: Q4343513
description: scientific article; zbMATH DE number 4079044