Asymptotic wave propagation in a non-Newtonian compressible fluid with small dissipation
type: Item
instance of: scholarly article
title: Asymptotic wave propagation in a non-Newtonian compressible fluid with small dissipation
zbMATH Open document ID: 0927.76090
DOI: 10.1023/A:1004326617677
author: C. Curró
author: Giovanna Valenti
published in: Journal of Engineering Mathematics
publication date: 1999-12-05T00:00:00Z
review text: A dissipative system describing the spherically symmetric motion of a non-Newtonian compressible fluid is considered to investigate the point-explosion problem. The effects of nonlinearity and dissipation involved in the model are studied by assuming an asymptotic expansion around a similarity solution of the associated hyperbolic system. In the far-field approximation, the authors derive an evolution equation which is different from the conventional Burgers-like equation in that the coefficient of the second-order derivative term involves an infinite series of the first order derivatives. A consistency argument for the obtained equation leads to some conditions on the viscosity coefficients. These restrictions allow the selection of the functional form of the constitutive equation. The authors consider different cases where the infinite series coefficients can be truncated. The obtained generalized equations do not admit exact analytic treatment, and one must study them by using matched asymptotic analysis, similarity analysis or numerical methods. The constitutive equations are too complicated for the study of the evolution equation. Thus the authors employ polynomial approximations of various degrees, where the coefficients of the constitutive equation are taken as polynomials of degree \(n\), \(n-1\), and \(n-2\) in the strain-tensor invariants I, II and III respectively. In the special case of Stokesian fluid of third order, it is possible to obtain several classes of solutions to the evolution equation. Finally, numerical results are presented for wave profiles for cylindrical and plane waves, and are compared with the results form the classical Burgers equation.
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 1281999
zbMATH Keywords: infinite series of first order derivatives
zbMATH Keywords: spherically symmetric motion
zbMATH Keywords: point-explosion problem
zbMATH Keywords: dissipation
zbMATH Keywords: hyperbolic system
zbMATH Keywords: far-field approximation
zbMATH Keywords: evolution equation
zbMATH Keywords: polynomial approximations
zbMATH Keywords: Stokesian fluid of third order
zbMATH Keywords: Burgers equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1281999