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# Owens, Robert Gwyn

Full Professor

Faculty of Arts and Science - Department of Mathematics and Statistics

514 343-2315

### Affiliations

• Membre Centre de recherches mathématiques

### Student supervision Expand allCollapse all

Modeling and Numerical Simulation of the clot detachment from a blood vessel wall Theses and supervised dissertations / 2018-01
Golyari, Sara
Abstract
In this thesis we propose a model to numerically study the behavior of blood, which is considered as an incompressible Newtonian fluid, in the presence of a clot attached to a vessel wall. The purpose of this study is to find out whether different flow regimes may cause a clot to detach from a vessel wall or it would lead to a stable state. In Chapter 1, we give a literature review of previous studies modeling blood coagulation, blood clots in the vascular system, platelet adhesion and aggregation and pathological clot formation. Our work is mainly based upon some part of the mathematical model given by Bajd and Serša [3], which is presented in Chapter 1. Then, we will describe the mathematical modeling of the fluid presenting the blood and the solid representing the clot in Chapter 2. The third chapter will focus on the numerical approach consisting of a projection method and the immersed boundary method [36] for solving the Navier-Stokes equations. Finally, in Chapter 4, we will discuss the results and give conclusions about the influence of different flow regimes on the clot stability.

Étude des discrétisations superconsistantes et application à la résolution numérique d'équations d'advection-diffusion Theses and supervised dissertations / 2017-12
De l'Isle, François
Abstract
This thesis develops the work of Fatone, Funaro et al. on superconsistent discretizations. We first give a precise definition of superconsistency and how it relates to consistency. We then suggest an explicit approach to constructing a superconsistent scheme from a linear operator and we apply the method to the advection-diffusion operator which we find, for example, in advective diffusive problems and the Navier Stokes equations. Both an analytical study and some numerical tests are provided. The choice of problems is made so that the diffusive term is small compared to the advective term. Solutions to such problems typically contain a boundary layer and classical centered finite difference methods may display some spurious oscillations in and near that layer. In contrast, solutions obtained with the superconsistent method are far more stable. In this work, only problems in one and two dimensions are treated since three dimensional problems would be too demanding on computational resources.

Méthode SPH implicite d'ordre 2 appliquée à des fluides incompressibles munis d'une frontière libre Theses and supervised dissertations / 2017-05
Rioux-Lavoie, Damien
Abstract
The objective of this thesis is to introduce a new implicit purely lagrangian smoothed particle hydrodynamics (SPH) method, for the resolution of the two-dimensional incompressible Navier-Stokes equations in the presence of a free surface. Our discretization scheme is based on that of Kéou Noutcheuwa et Owens [19]. We have treated the free surface by combining Yildiz et al. [43] multiple boundary tangent (MBT) method and boundary conditions on the auxiliary fields of Yang et Prosperetti [42]. In this way, we obtain a discretization scheme of order $\mathcal{O}(\Delta t ^2)$ and $\mathcal{O}(\Delta x ^2)$, according to certain constraints on the smoothing length $h$. First, we tested our scheme with a two-dimensional Poiseuille flow by means of which we analyze the discretization error of the SPH method. Then, we tried to simulate a two-dimensional Newtonian extrusion problem. Unfortunately, although the behavior of the free surface is satisfactory, we have encountered numerical problems on the singularity at the output of the die.

Simulation de la nage anguilliforme Theses and supervised dissertations / 2014-05
Lapierre, David
Abstract
This paper first discusses various attempts at modeling and simulating anguilliform swimming, then we develop a new technique, based on a method of generalized immersed boundary and the beam theory of Reissner-Simo. Subsequent to the derivation of the equations of polar fluids, the beam theory is derived from continuum mechanics and the resulting equations are then discretized, allowing a numerical solution. For the first time, the theory of additive Runge-Kutta schemes are combined with the Runge-Kutta-Munthe-Kaas method to generate schemes of arbitrarily high formal order of convergence. Moreover, the interpolation and spreading operations are handled from a new point of view that suggests the use of interpolatory nodal splines instead of spreading traditional functions. Finally, many numerical verifications are done before considering simulations of swimming.

Étude numérique des origines hémodynamiques des oscillations dans des réseaux de capillaires Theses and supervised dissertations / 2013-01
Tawfik, Yasmine
Abstract
While simulating blood flow in a microvascular network (in the absence of biological control), it is possible to observe the presence of oscillations in certain parameters such as blood flow, nodal pressure and hematocrit (red blood cell concentration in blood). This behaviour seems consistent with certain in vivo experiments. Despite this agreement, one has to wonder if the fluctuations observed in simulations are physical in nature, numerical or an artefact of unrealistic models since there are always differences between modelling and in vivo experiments. To settle this question satisfactorily, we will study and analyze blood flow and the nature of the fluctuations in different microvascular networks using a convective model and a well-mixed model to depict the governing equations for conservation of red blood cell mass. These models take into account two important rheological effects : the Fåhraeus-Lindqvist effect describing the apparent viscosity of blood flow in a vessel and the plasma skimming effect which describes the separation of red blood cells at diverging nodes. To describe the latter effect, we will implement two plasma skimming models (Pries et al. and Fenton et al.). In this thesis, we will present a description of the physiological problem (blood rheology). We will introduce the mathematical models used (well-mixed and convective) as well as the plasma skimming models (Pries et al. and Fenton et al.) accompanied by a detailed analysis of the numerical methods implemented. For the well-mixed model, we use the traditional explicit Euler method as well as a new implicit scheme that allows us to solve the problem in an efficient manner. This is done using a Newton-Krylov method with a preconditioned conjugate gradient and GMRES method for the inner iterations as well as a quasi- Newton method (Broyden’s method). The implicit method will include the vi backward Euler and trapezoidal methods. For the convective model, the explicit method of Kiani et al. will be implemented as well as a new numerical implicit approach. The stability of these numerical schemes will be explored. Using three different topologies, we will compare the results of the two mathematical models as well as the two plasma skimming models and the various numerical methods in order to ascertain to what extent the oscillations that have been observed using the traditional schemes may be attributable to the choice of the mathematical models or the choice of the numerical methods.

La méthode IIM pour une membrane immergée dans un fluide incompressible Theses and supervised dissertations / 2010-02
Morin-Drouin, Jérôme
Abstract
The Immersed Interface Method allows us to extend the scope of some numerical methods to discontinuous problems. Here we use it in the case of an incompressible fluid governed by the Navier-Stokes equations, in which a membrane is immersed, inducing a singular force. We use a projection method and staggered (MAC-type) finite difference approximations. A very complete derivation for the jump conditions is presented in the Appendix, for the case where the viscosity is continuous. Two numerical examples are shown : one without a membrane, and the other where the membrane is motionless. The general case of a moving membrane is also thoroughly studied.

Une nouvelle mise en oeuvre de la méthode IIM pour les équations de Navier-Stokes en présence d'une force singulière Theses and supervised dissertations / 2009
Conti, Marc
Abstract
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

### Selected publications Expand allCollapse all

#### On the jump conditions for the immersed interface method

M. Benoune, J. Morin-Drouin and R.G. Owens, On the jump conditions for the immersed interface method , (2014), , Journal

#### A mathematical and numerical investigation of the hemodynamical origins of oscillations in microvascular networks

Tawfik, Yasmine et Owens, Robert G., A mathematical and numerical investigation of the hemodynamical origins of oscillations in microvascular networks 75, 676--707 (2013), , Bull. Math. Biol.

#### A new incompressible smoothed particle hydrodynamics-immersed boundary method

Noutcheuwa, Rodrigue Kéou et Owens, Robert G., A new incompressible smoothed particle hydrodynamics-immersed boundary method 3, 126--167 (2012), , Int. J. Numer. Anal. Model. Ser. B

#### Computation of blood flows accounting for red-blood cell aggregation/fragmentation

A. S. Kane, Y. Bourgault, A. Lolov, R. G. Owens et A. Fortin, Computation of blood flows accounting for red-blood cell aggregation/fragmentation , 1-6 (2011), , Proceedings of the Seventh International Symposiom on the Turbulence and Shear Flow Phenomena (TSFP-7)

#### A mixed Brownian dynamics - SPH method for the simulation of flows of suspensions of bead-spring chains in confined geometries with hydrodynamic interaction

R. K. Noutcheuwa and R.G. Owens, A mixed Brownian dynamics - SPH method for the simulation of flows of suspensions of bead-spring chains in confined geometries with hydrodynamic interaction 166, 1327-1346 (2011), , J. Non-Newtonian Fluid Mech.

#### Some remarks on the equivalence of Kirkwood's diffusion equation and the coupled fluctuating polymer and solvent kinetic equation of Oono and Freed

A. Lozinski and R.G. Owens, Some remarks on the equivalence of Kirkwood's diffusion equation and the coupled fluctuating polymer and solvent kinetic equation of Oono and Freed 166, 1297-1303 (2011), , J. Non-Newtonian Fluid Mech.

#### The Langevin and Fokker-Planck Equations in Polymer Rheology

A. Lozinski, R. G. Owens and T.N. Phillips, The Langevin and Fokker-Planck Equations in Polymer Rheology Handbook of Numerical Analysis XVI, 2011-303 (2011), , Numerical Methods for Non-Newtonian Fluids, Elsevier North-Holland

#### A finite element method for a microstructure-based model of blood

Iolov, Alexandre, Kane, Abdoulaye S., Bourgault, Yves, Owens, Robert G. et Fortin, André, A finite element method for a microstructure-based model of blood 27, 1321--1349 (2011), , Int. J. Numer. Methods Biomed. Eng.

#### Kinetic models for dilute solutions of dumbbells in non-homogeneous flows

P. Degond, A. Lozinski and R. G. Owens, Kinetic models for dilute solutions of dumbbells in non-homogeneous flows 165, 509-518 (2010), , J. Non-Newtonian Fluid Mech.

#### Mathematical modelling of the cell-depleted peripheral layer in the steady flow of blood in a tube

M. A. Moyers-Gonzalez and R. G. Owens , Mathematical modelling of the cell-depleted peripheral layer in the steady flow of blood in a tube 47, 39-71 (2010), , Biorheology

#### Finite element methods for a mesoscopic constitutive model of blood

A. Lolov, Y. Bourgault, A. Fortin, A. Kane et R. G. Owens, Finite element methods for a mesoscopic constitutive model of blood , 1-4 (2009), , 1st International Conference on Mathematical and Computational Biomedical Engineering (CMBE2009), Swansea, UK, 29 juin au 1 juillet

#### On the high frequency oscillatory tube flow of healty human blood

M. Moyers-Gonzalez, R. G. Ownes et J. Fang, On the high frequency oscillatory tube flow of healty human blood 163, 45-61 (2009), , J. Non-Newtonian Fluid Mech.

#### Chapter 6: Rheological Models for Blood

A. Robertson, A. Séqueira et R. G. Owens, Chapter 6: Rheological Models for Blood , (2009), , Cardiovascular Mathematics, Springer-Verlag

#### A non-homogeneous constitutive model for human blood. I. Model derivation and steady flow

Moyers-Gonzalez, Miguel, Owens, Robert G. et Fang, Jiannong, A non-homogeneous constitutive model for human blood. I. Model derivation and steady flow 617, 327--354 (2008), , J. Fluid Mech.

#### Gelation time in the discrete coagulation-fragmentation equations with a bilinear coagulation kernel

Brunelle, Éric, Owens, Robert G. et van Roessel, Henry J., Gelation time in the discrete coagulation-fragmentation equations with a bilinear coagulation kernel 40, 11749--11764 (2007), , J. Phys. A

#### A novel fully-implicit finite volume method applied to the lid-driven cavity problem. I. High Reynolds number flow calculations

Sahin, Mehmet et Owens, Robert G., A novel fully-implicit finite volume method applied to the lid-driven cavity problem. I. High Reynolds number flow calculations 42, 57--77 (2003), , Internat. J. Numer. Methods Fluids

#### A novel fully-implicit finite volume method applied to the lid-driven cavity problem. II. Linear stability analysis

Sahin, Mehmet et Owens, Robert G., A novel fully-implicit finite volume method applied to the lid-driven cavity problem. II. Linear stability analysis 42, 79--88 (2003), , Internat. J. Numer. Methods Fluids

#### Computational rheology

Owens, R. G. and Phillips, T. N., Computational rheology , xvi+417 (2002), , Imperial College Press, London

#### An error indicator for mortar element solutions to the Stokes problem

Bernardi, Christine, Fiétier, Nicolas et Owens, Robert G., An error indicator for mortar element solutions to the Stokes problem 21, 857--886 (2001), , IMA J. Numer. Anal.

#### A new spectral element method for the reliable computation of viscoelastic flow

Chauvière, Cédric et Owens, Robert G., A new spectral element method for the reliable computation of viscoelastic flow 190, 3999--4018 (2001), , Comput. Methods Appl. Mech. Engrg.

#### A new adaptive modification strategy for numerical solutions to elliptic boundary value problems

Valenciano, José et Owens, Robert G., A new adaptive modification strategy for numerical solutions to elliptic boundary value problems 32, 305--329 (2000), , Appl. Numer. Math.

#### Spectral approximations on the triangle

Owens, R. G., Spectral approximations on the triangle 454, 857--872 (1998), , R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci.

#### A posteriori error estimates for spectral element solutions to viscoelastic flow problems

Owens, Robert G., A posteriori error estimates for spectral element solutions to viscoelastic flow problems 164, 375--395 (1998), , Comput. Methods Appl. Mech. Engrg.

#### Steady viscoelastic flow past a sphere using spectral elements

Owens, Robert G. et Phillips, Timothy N., Steady viscoelastic flow past a sphere using spectral elements 39, 1517--1534 (1996), , Internat. J. Numer. Methods Engrg.

#### Mass- and momentum-conserving spectral methods for Stokes flow

Owens, Robert G. et Phillips, Timothy N., Mass- and momentum-conserving spectral methods for Stokes flow 53, 185--206 (1994), , J. Comput. Appl. Math.

#### Compatible pseudospectral approximations for incompressible flow in an undulating tube

Owens, Robert G. et Phillips, Timothy N., Compatible pseudospectral approximations for incompressible flow in an undulating tube 37, 1181--1199 (1993), , J. Rheol.