Jean Deteix

• Professor at Université Laval

The incremental projection scheme and its enhanced version, the rotational projection scheme are powerful and commonly used approaches producing efficient numerical algorithms for solving the Navier–Stokes equations. However, the much improved rotational projection scheme cannot be used on models with non-homogeneous viscosity, imposing the use of...

Knowing the displacements of the solid boundary, various techniques have been proposed to update the fluid mesh in fluid–structure interaction problems. The ideal moving mesh method must be cheap, avoid the generation of degenerated elements and provide good quality elements to ease the finite element solution. We therefore introduce a very simple...

Continuation methods have proved to be very powerful tools when solving large finite element problems. However, implementation of these methods often require modifications to the standard finite element method. As a finite element code is already very complex, we would like to implement the continuation method as efficiently as possible. In this pa...

This paper presents a new algorithm for the numerical solution of the Navier--Stokes equations coupled with the convection-diffusion equation. After establishing convergence of the semi-discrete formulation at each time step, we introduce a new iterative scheme based on a projection method called the coupled prediction scheme. We show that even tho...

In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achie...

Nodes of Ranvier play critical roles in the generation and transmission of action potentials. Alterations in node properties during pathology and/or development are known to affect the speed and quality of electrical transmission. From a modelling standpoint, nodes of Ranvier are often described by systems of ordinary differential equations neglect...

In this work, we present an original time-discrete formulation of the coupled equations relating the velocity and pressure of an unsteady flow of two immiscible fluids and the Allen–Cahn equation describing the interface between both of them. We first prove this time-discrete formulation (based on the concept of coupled projection scheme (Deteix et...

Numerical modeling of phase change problems with convection is known to be computationally expensive. The main challenge comes from the coupling between Navier–Stokes and heat energy equations. In this paper, we develop a new scheme for phase change problems based on a projection method. The proposed method reduces the size of the system by splitti...

Numerical modeling of phase change problems with convection is known to be computationally expensive. The main challenge comes from the coupling between Navier-Stokes and heat energy equations. In this paper, we develop a new projection scheme suitable for these types of problems. The proposed method reduces the size of the system by splitting the...

This paper address the existence and uniqueness, in suitable functional spaces, of the solution of a non linear system of equations originating from the implicit time discretization of the coupled unsteady Navier-Stokes and Allen-Cahn equations. This result is based on the convergence analysis of an original stabilized fixed point algorithm, from w...

This work deals with shape optimization of an elastic body in sliding contact (Signorini) with a rigid foundation. The mechanical problem is written under its augmented Lagrangian formulation, then solved using a classical iterative approach. For practical reasons we are interested in applying the optimization process with respect to an intermediat...

In this article, the shape optimization of a linear elastic body subject to frictional (Tresca) contact is investigated. Due to the projection operators involved in the formulation of the contact problem, the solution is not shape differentiable in general. Moreover, shape optimization of the contact zone requires the computation of the gap between...

Combining the Navier–Stokes systems with Neumann (or natural) boundary condition to characterize a fluid flow is frequent. The popular projection (or pressure correction) methods inspired by Chorin and Temam are not well adapted to such boundary condition which translate in loss of accuracy. If some alternative projection methods have been proposed...

We introduce a new flexible mesh adaptation approach to efficiently compute a quantity of interest by the finite element method. By efficiently, we mean that the method provides an evaluation of that quantity up to a predetermined accuracy at a lower computational cost than other classical methods. The central pillar of the method is our scalar err...

The operator splitting approach applied to the Navier–Stokes equations gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called projection methods. The most basic of those schemes, the incremental and non-incremental variant (see Guermond...

This paper address the approximation of the dynamic of two fluids with non matching densities and viscosities modeled by the Allen-Cahn equation coupled with the time dependent Navier-Stokes equations. Existence, uniqueness and a maximum principle are obtained for a totally implicit semi-discrete in time formulation. These results are based on an o...

This paper address the approximation of the dynamic of two fluids with non matching densities and viscosities modeled by the Allen-Cahn equation coupled with the time dependent Navier-Stokes equations. Existence, uniqueness and a maximum principle are obtained for a totally implicit semi-discrete in time formulation. These results are based on an o...

Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst–Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred exper...

Detailed information on the dynamics of voltage-gated channels and on the simulation of the generation of an action potential. (PDF)

Fluid-structure interaction (FSI) problems occur when a potentially deformable solid interact with a surrounding fluid. The flow of the fluid deforms the solid and/or changes its position thus modifying the geometry of the fluid domain. In this paper, we present an Arbitrary Lagrangian Eulerian (ALE) formulation of FSI problems and we present a few...

We introduce a new algorithm, which we shall call Mixed Iteration, or by the acronym Mix-It, for the solution of saddle point problems arising from minimization problems under equality and/or inequality constraints. Such constrained problems are found in many applications and we shall be specially interested in contact problems in solid mechanics....

Engineered wood flooring (EWF) is a multilayer composite flooring product. The cross layered structure is designed to give good dimensional stability to the EWF under changing environmental conditions. However, during winter season in North America, the indoor relative humidity could decrease dramatically and generate an important cupping deformati...

In this study, coupled mechanical and heat and mass transfer models describing mat compression and heat and moisture transfer occurring during hot pressing of medium-density fiberboard mats are presented. The mat is considered an aging linear elastic material and is described by a mechanical model in three dimensions. Rheological properties of the...

A mathematical model describing heat and moisture transfer during hot pressing of medium-density fiberboard mats is presented. The model is based on conservation of energy, air mass, and water vapor mass, resulting in a three-dimensional unsteady-state problem in which mat properties and state variables vary in time and space. The conservation equa...

In North America, flooring strips are manufactured with grooves at the back. There are various reasons for these grooves but, historically, they were considered a strategy to reduce weight and transportation costs as well as improving dimensional stability. As no data are available to assess best practices in terms of performance, we have investiga...

The objective of this work was to estimate the impact of the variability of the medium-density fiberboard mat heat and moisture transfer properties on the results predicted by a numerical model of hot pressing. The three state variables of the model, temperature, air pressure, and vapor pressure, depend on parameters describing the material propert...

The hot pressing of MDF is a complex process involving several heat and mass transfer properties of the fiber mat. A sensitivity study of the heat and mass transfer model to the mat physical properties is performed in the current study. The mathematical model is based on the conservation of heat, air, and water vapor. The three state variables of t...

In this paper, the development of a numerical model for the ageing linear viscoelastic behaviour of material in the general three-dimension context is addressed. More precisely we propose an approach allowing the integration in pre-existing linear viscoelastic numerical tools (specifically the finite element method) and avoiding time step restricti...

The performance and quality of appearance layered wood composite products depend largely on their dimensional stability. Layers of various wood species and orientation and the presence of adhesive layers in such products may induce deformation following moisture content changes and reduce product value. In this context, research on the design and h...

Adhesive films used in layered wood-based composites have a significant impact on moisture movement and must be considered in models of such products. The objective of this study was to characterize the wood – adhesive interface and determine its impact on the hygromechanical behavior of engineered wood flooring (EWF). The radial water vapor diffus...

We propose to solve a shape optimization problem related to soil mechanics, the optimization of the stability of a slope by the use of a reinforcing material. The method presented will not use the derivative of the cost which will lead to technical problem related to the size of the discrete optimization problem. However the method will be quite ge...