Related papers: Viscoelastic flows with conservation laws
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions , and such that…
We pursue here the development of models for complex (viscoelastic) fluids in shallow free-surface gravity flows which was initiated by [Bouchut-Boyaval, M3AS (23) 2013] for 1D (translation invariant) cases. The models we propose are…
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…
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…
Maxwell's 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 rigorous proofs are lacking. The present note is a…
We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…
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…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…
A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited…
The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It may describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in…
Saint-Venant equations can be generalized to account for a viscoelastic rheology in shallow flows. A Finite-Volume discretization for the 1D Saint-Venant system generalized to Upper-Convected Maxwell (UCM) fluids was proposed in [Bouchut \&…
Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes. The theory behind the phenomenon is closely related…
The shallow-water equations of Saint-Venant, often used to model the long-wave dynamics of free-surface flows driven by inertia and hydrostatic pressure, can be generalized to account for the elongational rheology of non-Newtonian fluids…
The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…
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…
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the…
We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…
In this paper, we introduce a new approach for constructing robust well-balanced numerical methods for the one-dimensional Saint-Venant system with and without the Manning friction term. Following the idea presented in [R. Abgrall, Commun.…
Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applications in engineering, biomaterials, and…