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Analysis of Shear Layers in a Fluid with Temperature-Dependent Viscosity

Estep, D. J. and Verduyn Lunel, S. M. and Williams, R. D. (2001) Analysis of Shear Layers in a Fluid with Temperature-Dependent Viscosity. Journal of Computational Physics, 173 (1). pp. 17-60. ISSN 0021-9991. http://resolver.caltech.edu/CaltechCACR:2001.191

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Abstract

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. Howerver, experiments show that the flow of a fluid in which viscosity decreases as temperature increases tends to form shear layers, narrow regions in which the velocity of the fluid changes sharply. In general, adiabatic shear layers are observed not only in fluids but also in thermo-plastic materials subject to shear at a high-strain rate and in combustion and there is widespread interest in modeling their formation. In this paper, we investigate a well-known model representing a basic system of conservation laws for a one-dimensional flow with temperature-dependent viscosity using a combination of analytical and numerical tools. We present results to substantiate the claim that the formation of shear layers can only occur in solutions of the model when the viscosity decreases sufficiently quickly as temperature increases and we further analyze the structure and stability properties of the layers.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jcph.2001.6837DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021999101968378PublisherArticle
ORCID:
AuthorORCID
Williams, R. D.0000-0002-9145-8580
Additional Information:© 2001 Academic Press. Received 3 October 2000, Revised 12 April 2001. The research of D. Estep is partially supported by The National Science Foundation, DMS 9506519, and the North Atlantic Treaty Organization, CRG 970189. The research of S. Verduyn Lunel is partially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek, NWO 600-61-410, and the North Atlantic Treaty Organization, CRG 970189. The authors gratefully thank Andrew Stuart for advice on constructing numerical methods that preserve conserved quantities and Bert Peletier for stimulating discussions.
Group:Center for Advanced Computing Research
Funders:
Funding AgencyGrant Number
NSFDMS-9506519
North Atlantic Treaty Organization (NATO)CRG 970189
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)NWO 600-61-410
Subject Keywords:a posteriori error estimates, adaptive error control, blow-up, conservation laws, finite element methods, fluid flow, invariant rectangles, plane Couette flow, reaction-diffusion equations, residual errors, shear layers, temperature-dependent viscosity, thermal diffusion
Record Number:CaltechCACR:2001.191
Persistent URL:http://resolver.caltech.edu/CaltechCACR:2001.191
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28195
Collection:CaltechCACR
Deposited By: Imported from CaltechCACR
Deposited On:22 Nov 2004
Last Modified:14 Apr 2017 18:46

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