A viscoelastic flow model of Maxwell-type with a symmetric-hyperbolic formulation

TL;DR

This paper develops a symmetric-hyperbolic formulation of a Maxwell-type viscoelastic flow model to enable well-posed multi-dimensional simulations, extending previous work with new derivations and details.

Contribution

It introduces a symmetric-hyperbolic formulation for a Maxwell-type viscoelastic flow model, facilitating multi-dimensional analysis and well-posedness.

Findings

Derived a symmetric-hyperbolic form of the Maxwell model

Extended previous models with new detailed derivations

Supported multi-dimensional flow analysis

Abstract

Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell models allow one to define well motions mostly for one-dimensional flows only. To define unequivocal multi-dimensional viscoelastic flows (as solutions to well-posed initial-value problems) we advocated in [ESAIM:M2AN 55 (2021) 807-831] an upper-convected Maxwell model for compressible flows with a symmetrichyperbolic formulation. Here, that model is derived again, with new details.