Laboratoire Matière et Systèmes Complexes

There will be a live diffusion with Zoom :

Monday February 13th, 11h30 in room 454 A.

Please contact Michael Berhanu to attend the visio-seminar.

A new formulation of Maxwell’s model for multi-dimensional viscoelastic flows

Sébastien Boyaval

Laboratoire d’Hydraulique Saint-Venant (LHSV), Ecole des Ponts ParisTech, EDF’lab Chatou

and

Matherials, Inria Paris

Many Partial Differential Equations (PDEs) have been proposed to model viscoelastic flows. Seminal hyperbolic PDEs have been proposed by Maxwell in 1867 for 2D elastic fluids with stress relaxation, to ensure propagation of 1D shear waves at finite-speed while capturing the viscosity of real fluid continua. But actual computations of multi-dimensional viscoelastic flows using Maxwell’s PDEs have remained limited, at least without additional diffusion that blurs the hyperbolic character of Maxwell’s PDEs.

We propose a new system of PDEs to model 3D viscoelastic flows of Maxwell fluids. Our system is quasilinear and symmetric-hyperbolic, thereby ensuring propagation of waves at finite-speed. It is inspired by the K-BKZ integral reformulation of Maxwell PDEs (proposed independently by Kaye and Bernstein, Kearsley, Zapas), but it is more versatile because purely differential.

The new system essentially uses additional variables for the fluid material properties. It rigorously unifies fluid models with elastodynamics for compressible solids, and it can be manipulated for various applications of the viscoelastic flow concept in environmental hydraulics (shallow-water flows) or materials engineering (non-isothermal flows).