TL;DR
This paper revises Maxwell's constitutive relation for compressible viscoelastic fluids, demonstrating a hyperbolic PDE system with a relaxation structure that aligns with Newtonian viscosity in smooth flows.
Contribution
It formulates a new hyperbolic PDE system for Maxwell fluids with a relaxation structure and verifies compatibility with Newtonian viscosity.
Findings
The PDE system has a conservation-dissipation (relaxation) structure.
The system is symmetrizable hyperbolic.
Revised Maxwell's relations are compatible with Newton's law in smooth flows.
Abstract
In this paper, we revise Maxwell's constitutive relation and formulate a system of first-order partial differential equations with two parameters for compressible viscoelastic fluid flows. The system is shown to possess a nice conservation-dissipation (relaxation) structure and therefore is symmetrizable hyperbolic. Moreover, for smooth flows we rigorously verify that the revised Maxwell's constitutive relations are compatible with Newton's law of viscosity.
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