Archive for the ‘Publications’ Category

Understanding the effect of kinetic and mass transport processes in cathode agglomerates


A 2D(1D) multi-scale membrane electrode assembly mathematical model is proposed to study the effect of micro-scale transport losses due to catalyst aggregation in the cathode catalyst layer of a fuel cell. In order to develop an analytical expression for micro-scale transport losses, previous agglomerate models assumed an oxygen reduction reaction order of one and neglected any proton transport effects. In this article, a numerical micro-scale spherical ionomer-filled agglomerate model is integrated with a two-dimensional membrane electrode assembly model in order to develop a flexible framework to study different charge, mass, and kinetic transport models that cannot generally be analyzed with an analytical formulation. Results show that there is a significant interplay between scales and that changes in micro-scale agglomerate properties can significantly affect agglomerate effectiveness and current density distributions in the catalyst layer while not significantly affecting overall cell performance. Using the proposed framework, the effects of: a) proton conductivity inside agglomerates, b) a non-equilibrium oxygen dissolution boundary condition, and c) electrochemical models with different oxygen reaction orders, are studied.

Authors: M Moore, P Wardlaw, P Dobson, JJ Boisvert, A Putz, RJ Spiteri, M Secanell

Link: Here

A transition state theory for calculating hopping times and diffusion in highly confined fluids


Monte Carlo simulation is used to study the dynamical crossover from single file diffusion to normal diffusion in fluids confined to narrow channels. We show that the long time diffusion coefficients for a series of systems involving hard and soft interaction potentials can be described in terms of a hopping time that measures the time it takes for a particle to escape the cage formed by its neighbors in the pore. Free energy barriers for the particle hopping process are calculated and used to show that transition state theory effectively describes the hopping time for all the systems studied, over a range of pore diameters. Our work suggests that the combination of hopping times and transition state theory offers a useful and general framework to describe the dynamics of these highly confined fluids.


Authors: Surajith N Wanasundara, Raymond J Spiteri, Richard K Bowles

Download: HoppingTimes

Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator


This chapter reports on the design and analysis of two non-standard finite-
difference (NSFD) methods for solving the diffusion-free Brusselator system. The first NSFD
method is simulated using two different denominator functions. It is shown that, under certain
conditions, the first method exhibits spurious behaviour, such as failing to capture the correct
asymptotic stability properties of the unique fixed-point as well as the stable limit cycle of the
continuous-time diffusion-free Brusselator system. On the other hand, the second NSFD method, designed using a semi-exact discretization framework of Mickens, is shown to be elementary stable and dynamically consistent with the diffusion-free Brusselator system for sufficiently small timesteps. These theoretical results are illustrated via numerical simulations.

Authors: Andrew Kroshko, Oluwaseun Sharomi, Abba B Gumel, Raymond J Spiteri

Link: Here

Revisionist integral deferred correction with adaptive step-size control


Abstract Adaptive step-size control is a critical feature for the robust and efficient numerical
solution of initial-value problems in ordinary differential equations. In this paper, we show
that adaptive step-size control can be incorporated within a family of parallel time integrators
known as revisionist integral deferred correction (RIDC) methods. The RIDC framework
allows for various strategies to implement step-size control, and we report results from
exploring a few of them.


Authors: Andrew Christlieb, Colin Macdonald, Benjamin Ong, Raymond Spiteri

Link: Here

An analysis of errors caused by leakage currents and unintentional potential groundings in the electrical resistivity method


A common error in the electrical resistivity method occurs when a cable connecting to a current or potential electrode is inadvertently grounded at a point other than the intended electrode, thus creating an extra electrode. In this paper, we derive expressions for the magnitude of the induced error of the inadvertent electrode as a function of the position for a homogeneous infinite half-space for a general four-electrode array. We also derive a general expression for the magnitude of the error in terms of the current densities for ground with a general resistivity distribution. We compare the theoretical results for homogeneous ground with small-scale field surveys and find them to be in good agreement.

We show that the error in the measured apparent resistivity has a value that is proportional to the apparent resistivity for an array made up of the inadvertent electrode and the electrode to which it is connected. We find that the induced error becomes very large if the additional electrode is a current electrode and it is placed near a potential electrode or if it is a potential electrode and it is placed near a current electrode. The magnitude of the error is the same whether the additional electrode is a current electrode or a potential electrode. The induced error approaches a constant non-zero value as the additional electrode is moved towards infinity. Resistivity heterogeneity in the ground can either increase or decrease the error depending on the sensitivity of the array formed by the inadvertent electrode and the electrode to which it is connected.

Authors: S.L. Butler a, , L. Pitka  , R.J. Spiteri

Download: CurrentLeakage

A CPFD model for a bubbly biomass–sand fluidized bed


This study reports a computational particle fluid dynamics model for the numerical simulation of a sand fluidized
bed with 8 wt.% and 16 wt.% biomass loadings. The proposed CPFD model, based on a Barracuda framework, is validated using experimental data obtained in a 15.2 cm diameter bed with a 22.5 cm static height. This fluidized bed unit is equipped with a pair of fiber optic sensors allowing one to obtain both the bubble size and bubble velocity frequency distributions in an ample range of experimental conditions. In addition to this, the first-, second-, and third-order statistical moments of the bubble size and the bubble velocity distributions are calculated for each one of the operating conditions studied.

On this basis, the present study demonstrates that the proposed CPFD model reproduces the asymmetric character of both bubble size and bubble velocity distributions. In addition, the simulated and experimental bubble size and bubble velocity distributions yield close first-, second-, and third-order statistical moments. Accordingly, one can ascertain that the proposed CPFD model is quite satisfactory for establishing fluid flow patterns in sand biomass fluidized bed gasifiers.

Authors: F Fotovat, A Abbasi, RJ Spiteri, H de Lasa, J Chaouki

Download: BubblyBioMass

odeToJava: A PSE for the Numerical Solution of IVPs


Problem-solving environments (PSEs) offer a powerful yet flexible and convenient means for general experimentation with computational methods, algorithm prototyping, and visualization and manipulation of
data. Consequently, PSEs have become the modus operandi of many computational scientists and engineers. However, despite these positive aspects, PSEs typically do not offer the level of granularity required by the specialist or algorithm designer to conveniently modify the details. In other words, the level at which PSEs are black boxes is often still too high for someone interested in modifying an algorithm as opposed to trying an alternative.

In this article, we describe odeToJava, a Java-based PSE for initial-value problems in ordinary differential equations. odeToJava implements explicit and linearly implicit implicit-explicit Runge–Kutta methods with error and stepsize control and intra-step interpolation (dense output), giving the user control and flexibilityover the implementational aspects of these methods. We illustrate the usage and functionality of odeToJava by means of computational case studies of initial-value problems (IVPs).

Authors : Andrew Kroshko and Raymond Spiteri
Download : ODEToJava

Stable time integration suppresses unphysical oscillations in the bidomain model.


The bidomain model is a popular model for simulating electrical activity in cardiac tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing spatially averaged cellular reactions and a system of partial differential equations (PDEs) describing electrodiffusion on tissue level. Because of this multi-scale, ODE/PDE structure of the model, operator-splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical solution methods. Second-order methods can generally be expected to be more effective than first-order methods under normal accuracy requirements. However, the simplest and the most commonly applied second-order method for the PDE step, the Crank–Nicolson (CN) method, may generate unphysical oscillations. In this paper, we investigate the performance of a two-stage, L-stable singly diagonally implicit Runge–Kutta method for solving the PDEs of the bidomain model. Numerical experiments show that the enhanced stability property of this method leads to more physically realistic numerical simulations compared to both the CN and backward Euler methods.

Authors: Torabi Ziaratgahi, Marsh, Sundnes, Spiteri

Download: TorabiEtAl2014

A Runge–Kutta BVODE Solver with Global Error and Defect Control


Boundary value ordinary differential equations (BVODEs) are systems of ODEs with boundary conditions imposed at two or more distinct points. The global error (GE) of a numerical solution to a BVODE is the amount by which the numerical solution differs from the exact solution. The defect is the amount by which the numerical solution fails to satisfy the ODEs and boundary conditions. Although GE control is often familiar to users, the defect controlled numerical solution can be
interpreted as the exact solution to a perturbation of the original BVODE. Software packages based on GE control and on defect control are in wide use.
The defect control solver, BVP SOLVER, can provide an a posteriori estimate of the GE using Richardson extrapolation. In this paper, we consider three more strategies for GE estimation based on (i) the direct use of a higher order discretization formula (HO), (ii) the use of a higher order discretization formula within a deferred correction (DC) framework, and (iii) the product of an estimate of the maximum defect and an estimate of the BVODE conditioning constant, and demonstrate that the HO and DC approaches have superior performance. We also modify BVP SOLVER to introduce GE control.

Authors: Boisvert, Muir, and Spiteri

Download: BoisvertEtAl2013

Modelling and Simulation of the CLS Cryogenic System


This paper presents results pertaining to the numerical modelling of the cryo-genic system at the Canadian Light Source. The cryogenic system consists of a cryostat that houses a Radio Frequency (RF) cavity used for boosting the energy of an electron beam. For consistent operation of the RF cavity, it must be kept immersed in liquid helium at a constant level with the pressure in the gas space maintained to an accuracy of 1 mbar. An improvement to the cryostat model suggested in [1] using control volumes is described. The model and numerical method developed for the liquid helium supply and gaseous helium return lines are validated using two di erent cases, viz., the liquid helium  ow rate from the liquid helium transfer line and the gaseous helium  ow rate from the cryostat for various heater power input settings. The numerical method described here is signi cantly more accurate, ecient, and  exible than that used in [2] based on an iterative bisection method.

Authors: Chidambaranathan and Spiteri

Download: Chidambaranathan2013