### MIT Mathematics Postdoctoral Associate

Computational mechanics
Multiscale modelling
Model order reduction

### 8 Research

• #### Postdoctoral Associate in Mathematics2019 - Present

##### Massachusetts Institute of Technology, USA
###### BAEF & Gustave Boël - Sofina Fellow 2019

Prof. Laurent Demanet

Development of a hybrid framework combining data-driven and model-based methods for the study of corrosion-erosion phenomena

• #### FNRS Research Fellow2015 - 19

##### Université catholique de Louvain, Belgium - Ecole Centrale de Nantes, France

Prof. Roland Keunings (UCL) and Prof. Francisco Chinesta (ECN / ENSAM ParisTech)

PhD thesis: Multi-scale modelling of fibre suspensions: Particle inertia, confined flows and data-driven approach
PhD thesis in cotutelle between UCL and ECN

11-12/2018: Research stay with Prof. A. Ammar at ENSAM Angers, France

02-05/2019: Research stay at ESI Group Tokyo, Japan

• #### Visiting FellowSummer 2014 / Summer 2015 / Summer 2016

##### Massachusetts Institute of Technology, USA

Prof. Laurent Demanet and Dr. Leonardo Zepeda-Núñez

Implementation of a high performance solver for the Helmholtz equation with applications to seismic imaging and wave propagation.

###  Education

• #### Master of Engineering (M.Eng.) in Applied Mathematics2013 - 15

##### Université catholique de Louvain, Belgium

Summa cum laude

Specialization in "Modelling and simulation of physical systems"​ and "Numerical algorithms"​ with a focus on mathematical modelling of complex fluids and flows.

Master thesis: "Multiscale modelling of dilute suspensions: from confined fibres to rigid clusters composed of rods"
Supervisors: Prof. Roland Keunings and Prof. Francisco Chinesta

• #### Bachelor of Applied Science - Engineering (B.Eng.)2010 - 13

##### Université catholique de Louvain, Belgium

Summa cum laude

Major: Applied Mathematics, minor: Computer Science

### 9 Research publications

Below is a list of publications sorted out by topic:

Feel free to contact me for more information concerning my past and current research!

Material on this web site is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. Copyright holders claiming that the material available below is not in accordance with copyright terms and constraints are invited to contact the author by e-mail and ask him to remove the links to specific manuscripts.

###  PhD thesis

#### A. Scheuer PDFMulti-scale modelling of fibre suspensions: particle inertia, confined flows and data-driven approach

##### Université catholique de Louvain / Ecole Centrale de Nantes, October 2018

ABSTRACT   Suspensions of fibres and non-spherical particles are encountered in many fields ranging from engineering to biology, e.g. papermaking, composite manufacturing, pharmaceutical applications, red blood cells, food-processing and cosmetics industries, etc. Predicting the evolution of the orientation state of the particles is crucial to estimate the rheology of the suspension, that is its flow behaviour, as well as the final properties of the material. Jeffery's theory, describing the kinematics of a single particle immersed in an homogeneous flow of Newtonian fluid, lays the foundation for almost every models used today. Coarser representations, built upon this theory, have been introduced later to describe statistically the orientation state of the particles, either using a probability density function, or even moments of this function (Advani-Tucker orientation tensors). The assumptions underlying Jeffery's model are however quite restrictive to predict reliably what happens in fibre suspensions flows encountered in industrial processes. In this thesis, we first revisit this model, studying the impact of particle inertia and of confinement (wall effects) on the particle kinematics. In each case, we propose a multi-scale approach, but given the challenges to upscale the microscopic description to the macroscopic scale, we then came up with an innovative approach based on data-driven simulations to circumvent upscaling issues and inaccuracies introduced by macroscopic closure approximations. Finally, we developed efficient numerical methods to simulate fluid flows in thin geometries, considering, within the Proper Generalized Decomposition (PGD) framework, an in-plane/out-of-plane separated representation of the solutions of the incompressible Navier-Stokes equations.

###  Multi-scale modelling of fibre suspensions

Orientation of a fibre in a shear flow - confined (red) vs. unconfined (blue)

#### M. Perez, A. Scheuer, E. Abisset-Chavanne, F. Chinesta, R. Keunings  PDFA multi-scale description of orientation in simple shear flows of confined rod suspensions

##### Journal of Non-Newtonian Fluid Mechanics, 233, 61-74 (2016)

ABSTRACT   The multi-scale description of dilute or semi-dilute suspensions involving rods has been successfully accomplished and applied in many scenarios of industrial interest. Many processes involve, however, the flow of rod suspensions in very narrow gaps whose thickness is much smaller than the rod length. In these conditions, the evolution of rod orientation is expected to be affected by confinement effects. In the present work, we propose a multi-scale description of rod orientation in confined conditions and simple shear flows.

#### A. Scheuer, E. Abisset-Chavanne, F. Chinesta, R. Keunings  PDFSecond-gradient modelling of orientation development and rheology of dilute confined suspensions

##### Journal of Non-Newtonian Fluid Mechanics, 237, 54-64 (2016)

ABSTRACT   We address the extension of Jeffery’s model, governing the orientation of rods im- mersed in a Newtonian fluid, to confined regimes occurring when the thickness of the flow domain is narrower than the rod length. The main modelling ingredients concern: (i) the consideration of the rod interactions with one or both gap walls and their effects on the rod orientation kinematics; and (ii) the consideration of non- uniform strain rates at the scale of the rod, requiring higher-order descriptions. Such scenarios are very close to those encountered in real composites forming processes and have never been appropriately addressed from a microstructural point of view. We also show that confinement conditions affect the rheology of the suspension.

#### R. Mezher, M. Perez, A. Scheuer, E. Abisset-Chavanne, F. Chinesta, R. Keunings  PDFAnalysis of the Folgar & Tucker model for concentrated fibre suspensions in unconfined and confined shear flows via direct numerical simulation

##### Composites Part A, 91, 388-397 (2016)

ABSTRACT   The classical Jeffery model allows for the prediction of the flow-induced orientation in dilute fibre suspensions. In most industrial applications, however, fibre suspensions are concentrated and fibre-fibre interactions cannot be ignored any longer. These interactions have been traditionally modelled at the mesoscopic and macroscopic scales by introducing a phenomenological diffusion term inducing a randomizing effect. In the so-called Folgar & Tucker (F&T) model, widely used in applications, the diffusion coefficient is assumed to scale linearly with the flow intensity, the latter being described by the second invariant of the rate of strain tensor. Modifications and alternatives to the F&T model have been proposed in view of the difficulty for the F&T model to explain an apparent orientation delay observed experimentally in injection-moulded parts. The noticed deviations were attributed to the intense fibre-fibre interactions, thus pointing to the limitations of a phenomenological diffusion term for describing them. In the present work, we revisit the F&T model and compare its predictions with those obtained by simplified state-of-the-art direct numerical simulation (DNS) in unconfined and confined simple shear flows for a range of shear rates and concentrations, the latter ensuring intense fibre-fibre interactions. In unconfined flows, we find that the F&T model agrees quantitatively with the DNS results once an adequate closure relation is considered for approximating the fourth-order orientation tensor involved in the F&T model. Thus, the results seem to confirm, at least in simple shear flows, the F&T assumption for the form of the isotropic rotary diffusion function scaling linearly with the magnitude of the scalar rate of deformation. Also, a linear scaling of the diffusivity with the fibre concentration is observed. This conclusion remains unexpectedly valid under moderately-confined flow conditions as soon as an advanced fitted closure, like the IBOF, is considered within the F&T model. Other simpler closures (e.g. quadratic or hybrid), however, definitively fail to address confinement issues as also reported in our former work for the dilute regime. Obviously the validity of these conclusions depends on the validity of the considered state-of-the-art DNS, issue that remains at present an open question.

#### R. Ibañez, A. Scheuer, E. Lopez, E. Abisset-Chavanne, F. Chinesta, R. Keunings  PDFFrom elastic homogenization to upscaling of non-Newtonian fluid flows in porous media

##### International Journal of Material Forming, 11, 607-617 (2018)

ABSTRACT   Upscaling behaviors of heterogeneous microstructures to define macroscopic effective media is of major interest in many areas of computational mechanics, in particular those related to materials and processes engineering. In this paper, we explore the possibility of defining a macroscopic behavior manifold from microscopic calculations, and then use it directly for efficiently performing manifold-based simulations at the macroscopic scale. We consider in this work upscaling of non-Newtonian flows in porous media, and more particularly the ones involving short-fibre suspensions.

#### A. Scheuer, E. Abisset-Chavanne, F. Chinesta, R. Keunings  PDFMicroscopic modelling of orientation kinematics of non-spherical particles suspended in confined flows using unilateral mechanics

##### Comptes Rendus Mécanique, 346, 48-56 (2018)

ABSTRACT   The properties of reinforced polymers strongly depend on the microstructural state, that is, the orientation state of the fibres suspended in the polymeric matrix, induced by the forming process. Understanding flow-induced anisotropy is thus a key element to optimize both materials and process. Despite the important progresses accomplished in the modelling and simulation of suspensions, few works addressed the fact that usual processing flows evolve in confined configurations, where particles characteristic lengths may be greater than the thickness of the narrow gaps in which the flow takes place. In those circumstances, orientation kinematics models proposed for unconfined flows must be extended to the confined case. In this short communication, we propose an alternative modelling framework based on the use of unilateral mechanics, consequently exhibiting a clear analogy with plasticity and contact mechanics. This framework allows us to revisit the motion of confined particles in Newtonian and non-Newtonian matrices. We also prove that the confined kinematics provided by this model are identical to those derived from microstructural approaches (Perez et al. (2016)).

#### A. Scheuer, A. Ammar, E. Abisset-Chavanne, E. Cueto, F. Chinesta, R. Keunings, S.G. Advani  PDFData-driven upscaling of orientation kinematics in suspensions of rigid fibres

##### Computer Modeling in Engineering & Sciences, 117, 367-386 (2018)

ABSTRACT   Describing the orientation state of the particles is often critical in fibre suspension applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred due to their low computational cost. Closure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpredictable. In this work, our aim is to provide macroscopic simulations of orientation that are cheap, accurate and closure-free. To this end, we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre suspensions. Since the physics at the microscopic scale can be modelled reasonably enough, the idea is to conduct accurate offline direct numerical simulations at that scale and to extract the corresponding macroscopic descriptors in order to build a database of scenarios. During the online stage, the macroscopic descriptors can then be updated quickly by combining adequately the items from the database instead of relying on an imprecise macroscopic model. This methodology is presented in the well-known case of dilute fibre suspensions (where it can be compared against closure-based macroscopic models) and in the case of suspensions of confined or electrically-charged fibres, for which state-of-the-art closures proved to be inadequate or simply do not exist.

#### M. Perez, A. Scheuer, E. Abisset-Chavanne, A. Ammar, F. Chinesta, R. Keunings  PDFOn the multi-scale description of micro-structured fluids composed of aggregating rods

##### Continuum Mechanics and Thermodynamics, 31, 955-967 (2019)

ABSTRACT   When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus, the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and their impact on the flow in which they are immersed. In a former work, we addressed a first modelling framework of these clusters, assumed so dense that they were considered rigid and their kinematics (flow-induced rotation) were totally defined by a symmetric tensor $\mathbf c$ with unit trace representing the cluster conformation. Then, the rigid nature of the clusters was relaxed, assuming them deformable, and a model giving the evolution of both the cluster shape and its microstructural orientation descriptor (the so-called shape and orientation tensors) was proposed. This paper compares the predictions coming from those models with finer-scale discrete simulations inspired from molecular dynamics modelling.

#### A. Scheuer, G. Gregoire, E. Abisset-Chavanne, F. Chinesta, R. Keunings  PDFModelling the effect of particle inertia on the orientation kinematics of fibres and spheroids immersed in a simple shear flow

##### Computers and Mathematics with Applications, In press (2019)

ABSTRACT   Simulations of flows containing non-spherical particles (fibres or ellipsoids) rely on the knowl- edge of the equation governing the particle motion in the flow. Most models used nowadays are based on the pioneering work of Jeffery (1922), who obtained an equation for the motion of an ellipsoidal particle immersed in a Newtonian fluid, despite the fact that this model relies on strong assumptions: negligible inertia, unconfined flow, dilute regime, flow unperturbed by the presence of the suspended particle, etc. In this work, we propose a dumbbell-based model aimed to describe the motion of an inertial fibre or ellipsoid suspended in a Newtonian fluid. We then use this model to study the orientation kinematics of such particle in a linear shear flow and compare it to the inertialess case. In the case of fibres, we observe the appearance of periodic orbits (whereas inertialess fibres just align in the flow field). For spheroids, our model predicts an orbit drift towards the flow-gradient plane, either gradually (slight inertia) or by first rotating around a moving oblique axis (heavy particles). Multi-Particle Collision Dynamics (MPCD) simulations were carried out to assess the model predictions in the case of inertial fibres and revealed similar behaviours.

###  3D Helmholtz equation

Solution of the Helmholtz equation for the SEAM model

PDF

#### L. Zepeda Núñez, A. Scheuer, R. J. Hewett, L. Demanet The method of polarized traces for the 3D Helmholtz equation

##### Geophysics, 84, 313-333 (2019)

ABSTRACT   We present a fast solver for the 3D Helmholtz equation, in heterogeneous, constant density, acoustic media, in the high-frequency regime. The solver is based on the method of polarized traces, a layered domain-decomposition method, where the subdomains are connected via transmission conditions prescribed by the discrete Green's representation formula and artificial reflections are avoided by enforcing non-reflecting boundary conditions between layers. The method of polarized traces allows us to consider only unknowns at the layer interfaces, reducing the overall cost and memory footprint of the solver. We demonstrate that polarizing the wavefields in this manner yields an efficient preconditioner for the reduced system, whose rate of convergence is \textit{independent} of the problem frequency. The resulting preconditioned system is solved iteratively using GMRES, where we never assemble the reduced system or preconditioner, rather we implement them via solving the Helmholtz equation locally within the subdomains. The method is parallelized using MPI and coupled with a distributed linear algebra library and pipelining to obtain an empirical on-line runtime $\cO(\max(1,R/L) N \log N)$ where $N = n^3$ is the total number of degrees of freedom, $L$ is the number of subdomains, and $R$ is the number of right-hand sides. This scaling is favorable for regimes in which the number of sources (distinct right-hand sides) is large, for example enabling large-scale implementations of \LZ{frequency-domain} full waveform inversion (FWI).

###  Unclassified

#### E. Lopez, A. Scheuer, E. Abisset-Chavanne, F. Chinesta  PDFOn the effect of phase transition on the manifold dimensionality: Application to the Ising model

##### Mathematics and Mechanics of Complex Systems, 6, 251-265 (2018)

ABSTRACT   Fields can be represented in a discrete manner from their values at some locations, the nodes when considering finite elements descriptions. Thus, each discrete scalar solution can be considered as a point in $\mathbb R^N$ ($N$ being the number of nodes used for approximating the scalar field). Most manifold learning techniques (linear and nonlinear) are based on the fact that those solutions define a slow manifold of dimension $n \ll N$ embedded in the space $\mathbb R^N$. This paper explores such a behaviour in systems exhibiting phase transitions in order to analyse the evolution of the local dimensionality $n$ when the system moves from one side of the critical behaviour to the other. For that purpose we consider the Ising model.

#### R. Ibañez, A. Scheuer, E. Abisset-Chavanne, F. Chinesta, A. Huerta, R. Keunings  PDFA simple microstructural viscoelastic model for flowing foams

##### International Journal of Material Forming, 12, 295-306 (2019)

ABSTRACT   The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed by the macroscopic flow kinematics.

### s Music

I enjoy playing the cello and am a former member of the Louvain-la-Neuve Student Symphony Orchestra (OSEL).

### ` Contact info

• Massachusetts Institute of Technology
MIT Mathematics / Earth Resources Laboratory
Green Building - Office 54-323
77 Massachusetts Avenue
02139 Cambridge, MA
United States

• Email: ascheuer [at] mit.edu
• http://math.mit.edu/~ascheuer/