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A hyperbolic model for viscous Newtonian flows

Peshkov, Ilya ; Romenski, Evgeniy

Continuum mechanics and thermodynamics, 2016-03, Vol.28 (1-2), p.85-104 [Peer Reviewed Journal]

Berlin/Heidelberg: Springer Berlin Heidelberg

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  • Title:
    A hyperbolic model for viscous Newtonian flows
  • Author: Peshkov, Ilya ; Romenski, Evgeniy
  • Subjects: Classical and Continuum Physics ; Coefficients ; Continuums ; Engineering Thermodynamics ; Fluid mechanics ; Heat and Mass Transfer ; Mathematical models ; Navier-Stokes equations ; Original Article ; Physics ; Physics and Astronomy ; Shear ; Shear flow ; Sound velocity ; Structural Materials ; Theoretical and Applied Mechanics ; Thermodynamics ; Viscosity ; Viscous fluids
  • Is Part Of: Continuum mechanics and thermodynamics, 2016-03, Vol.28 (1-2), p.85-104
  • Notes: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Description: 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.
  • Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
  • Language: English
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