7th AMARENA DaYs

Amiens-Milano-poitiers REunion on Numerical and mathematical Analysis

May 15 - 16 2019

7th AMARENA DaYs

Amiens-Milano-poitiers REunion on Numerical and mathematical Analysis

May 15 - 16 2019

Laboratoire Amiénois de Mathématique

Fondamentale et Appliquée

CNRS UMR 7352

Program

Salle de thèses

Ecole doctorale STS, UPJV

First day: Wednesday 15

9h Welcome

9h30-10h15 Maurizio Grasselli (Politecnico Milano)

Incompressible binary fluids with unmatched densities and moving contact lines

10h15-11h Monica Conti (Politecnico Milano)

Decay properties of linear Volterra integro-differential equations

11h-11h15 : break

11h15 -12h Olivier Goubet (LAMFA, UPJV)

Analyticity of the global attractor for damped forced periodic Korteweg-de Vries equation

12h-14h : lunch

14h-14h45 Cecilia Cavaterra (Università statale di Milano)

Long-time dynamics and optimal control of a diffuse interface model for tumor growth

15h-15h45 discussion

Second day: Thursday 16

9h Welcome

9h30-10h15 Alexis Rucci (LRCS, UPJV)

Microstructural-resolved modeling of Lithium Ion Batteries, from fabrication to cell performance prediction

10h15-11h Filippo Dell'Oro (Politecnico Milano)

Asymptotic behavior of Benjamin-Bona-Mahony equations with dissipative memory

11h-11h15 break

11h15 -12h Caterina Calgaro (Laboratoire Paul Painlevé, Université de Lille)

Analysis and approximation by a combined finite volume - finite element method of a low Mach combustion model

12h-14h : lunch

14h-14h45 Vittorino Pata (Politecnico Milano)

Two questions arising in the theory of attractors

15h-15h45 discussion and closure

Abstracts

Maurizio Grasselli:
Incompressible binary fluids with unmatched densities and moving contact lines

The motion of an isothermal mixture of two immiscible and incompressible fluids subject to phase separation can be described by the well-known model H. This is a diffuse interface model which consists of the Navier-Stokes equations for the (volume) average velocity which are subject to a force depending on the difference of the relative concentrations of the two fluids. The evolution of this concentration is governed by a convective Cahn-Hilliard equation. The system is also known as Cahn-Hilliard-Navier-Stokes (CHNS) system. In the existing literature there are many theoretical results on CHNS systems equipped with no-slip (or periodic) boundary conditions for the fluid velocity and no-flux (or periodic) boundary conditions for the concentration and the chemical potential. However, it has been observed that the moving contact line, defined as the intersection of the fluid-fluid interface with the solid wall, is incompatible with the no-slip boundary condition. More precisely, there is a velocity discontinuity at the moving contact line, and the tangential force exerted by the fluids on the solid surface in the vicinity of the contact line becomes infinite. Thus, in immiscible two-phase flows, none of the mentioned boundary conditions can account for the moving contact line slip velocity profiles obtained from experiments. I intend to discuss a CHNS system for compressible binary fluids with different (unmatched) densities proposed by Abels, Garcke, and Gruen in 2012, but endowed with boundary conditions which account for moving contact lines.

Monica Conti:
Decay properties of linear Volterra integro-differential equations

We discuss some results concerning theexponential decay and the polynomial decay of the energy associated with linear Volterra integro-differential equations. In particular, we provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel.

Olivier Goubet: Analyticity of the global attractor for damped forced periodic Korteweg-de Vries equation

We provide a proof of the analyticity of the global attractor
for dissipative damped KdV equations and we describe some consequences of this new result.

Cecila Cavaterra: Long-time dynamics and optimal control of a diffuse interface model for tumor growth

We investigate the long-time dynamics and an optimal control problem of a diffuse interface model describing the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type equation for the tumor cell fraction and a reaction-diffusion equation for the nutrient.

Alexis Rucci: Microstructural-resolved modeling of Lithium Ion Batteries, from fabrication to cell performance prediction.

Practical properties of LIBs, namely their energy density, recharging time, durability and safety depend, amongst other features, on the negative and positive electrode mesostructure. The latter is characterized by the spatial location of the active material particles, carbon additive aggregates and polymeric binder, which form the composite electrodes. In this presentation we discuss in house approaches for the incorporation of three-dimensional-resolved LiNixMnxCoxO2 (x=1/3, NMC)-based electrode mesostructures into COMSOL Multiphysics where a 3D extension of the Newman model was implemented in order to account for the performance (i.e. discharge process) at the cell level for different electrode formulations. On a second hand, we discuss algorithmic aspects within a study of the influence in the final cell performance of the cathode mesostructure, taking into account different geometrical aspects such as the particles spatial distribution and their location uncertainties. We introduce in this presentation the recently developed tool INNOV, an in house code able to mesh several phases, applied to the separation of AM and CBD in an electrode mesostructure, in order to capture the influence of the conductive media in the final cell performance. Results reveal that the model captures the main experimental features determining the performance of the Li-ion electrode in terms of its formulation, starting from the simulation of the fabrication process towards the prediction of the final cell performance, showing a good agreement with experimental measurements. All these studies are carried out in the ARTISTIC ERC project.

Filippo Dell'Oro: Asymptotic behavior of Benjamin-Bona-Mahony equations with dissipative memory

We investigate the asymptotic properties of the nonlinear solution semigroup generated by the Benjamin-Bona-Mahony equation with dissipative memory. In particular, under a suitable smallness assumption on the external force, we show that the semigroup possesses the global attractor in the natural weak energy space. The result is obtained by means of a nonstandard approach based on the construction of a suitable family of attractors on certain invariant sets of the phase space.

Caterina Calgaro: Analysis and approximation by a combined finite volume - finite element method of a low Mach combustion model

Various phenomena such as convective and conductive heat transfert or combustion processes can be described by a low Mach model. This model allows to generate intermediate solutions between the compressible Navier-Stokes model and the incompressible Navier-Stokes one. In a first part, we are interested in a specific low-Mach model for which the dynamic viscosity of the fluid is a specific function of the density. The model is reformulated in terms of temperature and velocity, where the temperature equation is non-linear. A local-in-time existence result for strong solutions of the Cauchy problem is proposed and some convergence rates of the error between the approximation and the exact solution are obtained. In a second part, we develop a numerical scheme which combines Finite Volumes and Finite Elements methods to simulate some more general low-Mach flows. The continuity equation is solved by a Finite Volume method, while the momentum and temperature equations are solved by Finite Elements, with the compressibility constraint solved by a projection scheme. This scheme ensure the preservation of constant states. Our results are compared to some of the literature by simulating a transient injection flow in a 2D-domain as well as a natural convection flow in a 2D-cavity.

Vittorino Pata: Two questions arising in the theory of attractors

In this talk we dwell on the notions of global and exponential attractors
for strongly continuous semigroups acting on a complete metric space.
Two natural questions arising in the theory are addressed.