A hyperbolic model for viscous Newtonian flows

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• 作者：Ilya Peshkov ; Evgeniy Romenski
• 关键词：Hyperbolic equations ; Navier–Stokes equations ; Solid dynamics ; Viscous fluids ; Irreversible deformation ; Thermodynamics ; Non ; equilibrium flows
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：28
• 期：1-2
• 页码：85-104
• 全文大小：884 KB
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• 作者单位：Ilya Peshkov (1)
  Evgeniy Romenski (2) (3)
  
  1. IUSTI UMR 7343, CNRS, Aix Marseille Université, Marseille, France
  2. Sobolev Institute of Mathematics, Novosibirsk, Russia
  3. Novosibirsk State University, Novosibirsk, Russia
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Engineering Thermodynamics and Transport Phenomena
  Mechanics, Fluids and Thermodynamics
  Structural Materials
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0959

文摘

We discuss a pure hyperbolic alternative to the Navier–Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first-order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use of the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of material particles connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows, arbitrary incompressible and compressible flows of Newtonian fluids and demonstrate that Newton’s viscous law can be obtained in the framework of the developed hyperbolic theory as a steady-state limit. A basic relation between the viscosity coefficient, PSL time, and the shear sound velocity is also obtained. Keywords Hyperbolic equations Navier–Stokes equations Solid dynamics Viscous fluids Irreversible deformation Thermodynamics Non-equilibrium flows