Related papers: Visco-elastodynamics at large strains Eulerian
Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We…
Rock and ice are ubiquitous geologic materials. While apparently solid, they also exhibit fluid behavior under stress - a property termed viscoelasticity. Viscoelastic convection of Earth's mantle drives tectonic plate motion with…
The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volume integrals. The terms can lead to aliasing and stability…
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…
This paper is devoted to study the phase space analysis of isotropic and homogenous universe model by taking a noninteracting mixture of electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of…
We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain…
We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element, with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies…
We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…
We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and…
A nonlinear viscoelastic theory of nematodynamic type is developed for nematic liquid crystalline (LC) semi-flexible polymers. A measure of transient elastic strain due to the change in length of macromolecular strands under stress, and the…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…
The aim of this paper is to present a modeling for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory (Ref. 6) is first generalized to take into account…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…
We propose a nonconforming finite element method for isentropic viscous gas flow in situations where convective effects may be neglected. We approximate the continuity equation by a piecewise constant discontinuous Galerkin method. The…
We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field…
We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…