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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the unsteady, stagnation point flow of a Maxwell fluid in 2D

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Author(s):
Moshkin, N. P. [1, 2] ; Pukhnachev, V. V. [1, 2] ; Bozhkov, Yu D. [3]
Total Authors: 3
Affiliation:
[1] Russian Acad Sci, Siberian Branch, Lavrentyev Inst Hydrodynam, 15 Ac Lavrentyev Ave, Novosibirsk 630090 - Russia
[2] Novosibirsk State Univ, 90, 1 Pirogov Str, Novosibirsk 630090 - Russia
[3] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Campinas, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS; v. 116, p. 32-38, NOV 2019.
Web of Science Citations: 0
Abstract

A two-dimensional unsteady stagnation-point flow of an incompressible viscoelastic fluid is studied theoretically assuming that the fluid obeys the upper convected Maxwell model. To achieve better understanding of the main properties of the governing equations, the system of non-linear equations is transformed to Lagrangian variables. As a result, a closed system of equations of the mixed elliptic-hyperbolic type is obtained. These equations are decomposed into a hyperbolic submodel and a quadrature. The hyperbolic part is responsible for the transport of nonlinear transverse waves in an incompressible Maxwell medium. The system of equations guarantees the existence of the energy integral, which allows one to analyze discontinuous solutions to these equations. It is demonstrated that solutions with strong discontinuities are impossible, though a solution with weak discontinuities can exist. Several numerical examples of the problems of practical interest show that perturbations induced by weak discontinuities in the initial data propagate with a finite speed, which confirms the hyperbolic character of the system. (AU)

FAPESP's process: 12/21475-4 - Group analysis of nonlinear viscoelastic media equations
Grantee:Yuri Dimitrov Bozhkov
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 15/24589-9 - Nonlinear Analysis and Applications
Grantee:Yuri Dimitrov Bozhkov
Support Opportunities: Regular Research Grants