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

Autor(es)

Moshkin, N. P. ^{[1, 2]} ; Pukhnachev, V. V. ^{[1, 2]} ; Bozhkov, Yu D. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS; v. 116, p. 32-38, NOV 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 12/21475-4 - Grupo-análise de EDPs não-lineares em viscoelasticidade
• Beneficiário: Yuri Dimitrov Bozhkov
• Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 15/24589-9 - Análise não-linear e aplicações
• Beneficiário: Yuri Dimitrov Bozhkov
• Linha de fomento: Auxílio à Pesquisa - Regular