Um corpo imerso em movimento arbitrário interage com o fluido ao redor. As partículas fluidas próximas ao corpo exercem certa resistência inercial quando o corpo acelera ou desacelera, devido ao acoplamento dinâmico entre corpo e fluido. Este trabalho resolve as equações de Navier-Stokes, discretizadas pelo método dos elementos finitos, usando o programa de código aberto (LGPL) FreeFem++, e avalia as forças do escoamento que agem sobre um cilindro circular, o qual oscila harmonicamente em um fluido em repouso para números de Keulegan-Carpenter (KC) entre 0,5 e 10, mantendo o parâmetro da frequência constante e igual a 35. Os números de KC selecionados visam entender os conceitos de inércia adicional em fluido viscoso, desde em escoamentos simples até em escoamento mais complexos. O escoamento é bidimensional, laminar e não estacionário. A força em linha com o movimento é então decomposta, conforme equação de Morison, como a soma de uma força inercial e outra de arrasto. Os resultados possuem boa aderência com trabalhos analíticos, experimentais e numéricos anteriores disponíveis na literatura. A dinâmica do escoamento induzido pelo cilindro em movimento harmônico é rica. Para baixo KC, o escoamento é simétrico e estável. Para valores intermediários de KC, a camada limite descola da superfície do cilindro e vórtices são emitidos a cada meio-ciclo. Para elevado KC, certa assimetria se desenvolve e vórtices são emitidos obliquamente a cada meio-ciclo. / An immersed body in arbitrary motion interacts with the surrounding fluid. The fluid particles close to the body impart their inertial resistance when the body accelerates or decelerates, due to the dynamic coupling between body and fluid. This work solves the incompressible Navier-Stokes equation, discretized by the finite element method, using the open source (LGPL) software FreeFem++, and evaluates the flow forces that act on a circular cylinder which oscillates harmonically in a resting fluid for Keulegan- Carpenter (KC) number between 0.5 and 10, with a constant frequency parameter equal to 35. The selected KC numbers aims to understand the concepts of added inertia in viscous fluid, from simpler to more complex flows. The flow is two dimensional, laminar and unsteady. The in-line force is then decomposed, according to Morison equation, as a sum of an inertial force and a drag force. The results agree with former analytical, experimental and numerical works available in the literature. The dynamics of the flow induced by the harmonically moving cylinder is rich. For low KC, the flow is symmetric and stable. For intermediate KC, the boundary layer detaches from the cylinder surface and vortices are shed at each half cycle. For higher KC, certain asymmetry develops and vortices are shed obliquely at each half cycle.

Um corpo imerso em movimento arbitrário interage com o fluido ao redor. As partículas fluidas próximas ao corpo exercem certa resistência inercial quando o corpo acelera ou desacelera, devido ao acoplamento dinâmico entre corpo e fluido. Este trabalho resolve as equações de Navier-Stokes, discretizadas pelo método dos elementos finitos, usando o programa de código aberto (LGPL) FreeFem++, e avalia as forças do escoamento que agem sobre um cilindro circular, o qual oscila harmonicamente em um fluido em repouso para números de Keulegan-Carpenter (KC) entre 0,5 e 10, mantendo o parâmetro da frequência constante e igual a 35. Os números de KC selecionados visam entender os conceitos de inércia adicional em fluido viscoso, desde em escoamentos simples até em escoamento mais complexos. O escoamento é bidimensional, laminar e não estacionário. A força em linha com o movimento é então decomposta, conforme equação de Morison, como a soma de uma força inercial e outra de arrasto. Os resultados possuem boa aderência com trabalhos analíticos, experimentais e numéricos anteriores disponíveis na literatura. A dinâmica do escoamento induzido pelo cilindro em movimento harmônico é rica. Para baixo KC, o escoamento é simétrico e estável. Para valores intermediários de KC, a camada limite descola da superfície do cilindro e vórtices são emitidos a cada meio-ciclo. Para elevado KC, certa assimetria se desenvolve e vórtices são emitidos obliquamente a cada meio-ciclo. / An immersed body in arbitrary motion interacts with the surrounding fluid. The fluid particles close to the body impart their inertial resistance when the body accelerates or decelerates, due to the dynamic coupling between body and fluid. This work solves the incompressible Navier-Stokes equation, discretized by the finite element method, using the open source (LGPL) software FreeFem++, and evaluates the flow forces that act on a circular cylinder which oscillates harmonically in a resting fluid for Keulegan- Carpenter (KC) number between 0.5 and 10, with a constant frequency parameter equal to 35. The selected KC numbers aims to understand the concepts of added inertia in viscous fluid, from simpler to more complex flows. The flow is two dimensional, laminar and unsteady. The in-line force is then decomposed, according to Morison equation, as a sum of an inertial force and a drag force. The results agree with former analytical, experimental and numerical works available in the literature. The dynamics of the flow induced by the harmonically moving cylinder is rich. For low KC, the flow is symmetric and stable. For intermediate KC, the boundary layer detaches from the cylinder surface and vortices are shed at each half cycle. For higher KC, certain asymmetry develops and vortices are shed obliquely at each half cycle.

Este trabalho aborda a solução numérica das equações lineares de águas rasas. O método dos elementos finitos e utilizado para a discretização espacial das equações que modelam o problema, e para a discretização temporal, o esquema semi-implícito de Crank-Nicolson é empregado. Além de alguns conceitos comuns quando se trabalha com escoamentos geofísicos, são descritas também a formulação das equações de águas rasas, sua linearização e uma solução analítica para um caso onde o parâmetro de Coriolis é nulo. A escolha adequada de pares de elementos finitos é a principal dificuldade quando se trabalha com esse método para a resolução da equação de águas rasas. Assim, é discutido o uso de quatro pares de elementos finitos e técnicas de estabilização para contornar o surgimento de modos espúrios na solução discreta. Os resultados numéricos são realizados com auxílio do software FreeFem++, onde se pode notar a capacidade dos pares de elementos de reproduzirem o escoamento, através da solução discreta, além das propriedades de conservação de massa e energia de cada discretização. / This work is about the numerical solution of the linear shallow water equations. The finite element method is used for spatial discretization of the equations that model the problem and for the time discretization the semi-implicit Crank-Nicolson scheme is used. Besides the concepts related to geophysical flows, the formulation of the shallow water equations, their linearization and an analytical solution for a case where the Coriolis parameter is zero are also described. The appropriate choice of a pair of finite elements is the main difficulty when working with this method for solving the shallow water equations. The use of four pairs of finite elements and stabilization techniques to circumvent the appearance of spurious modes in the discrete solution are discussed. The numerical results are performed using the software FreeFem++, where one can notice the ability of the elements to represent the discrete solution and mass and energy conservation of each discretization.

Este trabalho aborda a solução numérica das equações lineares de águas rasas. O método dos elementos finitos e utilizado para a discretização espacial das equações que modelam o problema, e para a discretização temporal, o esquema semi-implícito de Crank-Nicolson é empregado. Além de alguns conceitos comuns quando se trabalha com escoamentos geofísicos, são descritas também a formulação das equações de águas rasas, sua linearização e uma solução analítica para um caso onde o parâmetro de Coriolis é nulo. A escolha adequada de pares de elementos finitos é a principal dificuldade quando se trabalha com esse método para a resolução da equação de águas rasas. Assim, é discutido o uso de quatro pares de elementos finitos e técnicas de estabilização para contornar o surgimento de modos espúrios na solução discreta. Os resultados numéricos são realizados com auxílio do software FreeFem++, onde se pode notar a capacidade dos pares de elementos de reproduzirem o escoamento, através da solução discreta, além das propriedades de conservação de massa e energia de cada discretização. / This work is about the numerical solution of the linear shallow water equations. The finite element method is used for spatial discretization of the equations that model the problem and for the time discretization the semi-implicit Crank-Nicolson scheme is used. Besides the concepts related to geophysical flows, the formulation of the shallow water equations, their linearization and an analytical solution for a case where the Coriolis parameter is zero are also described. The appropriate choice of a pair of finite elements is the main difficulty when working with this method for solving the shallow water equations. The use of four pairs of finite elements and stabilization techniques to circumvent the appearance of spurious modes in the discrete solution are discussed. The numerical results are performed using the software FreeFem++, where one can notice the ability of the elements to represent the discrete solution and mass and energy conservation of each discretization.

Este trabalho aborda a solução numérica das equações lineares de águas rasas. O método dos elementos finitos e utilizado para a discretização espacial das equações que modelam o problema, e para a discretização temporal, o esquema semi-implícito de Crank-Nicolson é empregado. Além de alguns conceitos comuns quando se trabalha com escoamentos geofísicos, são descritas também a formulação das equações de águas rasas, sua linearização e uma solução analítica para um caso onde o parâmetro de Coriolis é nulo. A escolha adequada de pares de elementos finitos é a principal dificuldade quando se trabalha com esse método para a resolução da equação de águas rasas. Assim, é discutido o uso de quatro pares de elementos finitos e técnicas de estabilização para contornar o surgimento de modos espúrios na solução discreta. Os resultados numéricos são realizados com auxílio do software FreeFem++, onde se pode notar a capacidade dos pares de elementos de reproduzirem o escoamento, através da solução discreta, além das propriedades de conservação de massa e energia de cada discretização. / This work is about the numerical solution of the linear shallow water equations. The finite element method is used for spatial discretization of the equations that model the problem and for the time discretization the semi-implicit Crank-Nicolson scheme is used. Besides the concepts related to geophysical flows, the formulation of the shallow water equations, their linearization and an analytical solution for a case where the Coriolis parameter is zero are also described. The appropriate choice of a pair of finite elements is the main difficulty when working with this method for solving the shallow water equations. The use of four pairs of finite elements and stabilization techniques to circumvent the appearance of spurious modes in the discrete solution are discussed. The numerical results are performed using the software FreeFem++, where one can notice the ability of the elements to represent the discrete solution and mass and energy conservation of each discretization.

Les eaux souterraines constituent 95% de l'eau douce accessible sur le globe. Les rapports de ``UNEP'' prédisent qu'en année 2020, 75% de la population mondiale vivra dans des zones côtières. Ces deux informations nous montrent l'importance des aquifères côtiers qui sont aujourd'hui surexploités. Cette surexploitation conduit à l'aggravation du phénomène naturel de l'intrusion saline. Sa modélisation est nécessaire pour évaluer et prédire l'étendue des zones impactées. Ce travail concerne la modélisation de l'intrusion saline dans l'aquifère de Tripoli-Liban. Cette ville est sur la mer Méditerranée et dans laquelle habite un huitième de la population libanaise (600,000). Dans cette étude, un modèle mathématique de l'intrusion saline dans l'aquifère de Tripoli est développé, en se basant sur l'implémentation de l'approche de l'interface abrupte dans ``Freefem++''. Ce modèle fournit principalement la profondeur de l'interface eau douce/eau salée. Les limites du modèle sont exposées et le modèle est validé avec la solution analytique, avec le code de calcul BFSWIM et avec les mesures de terrain où l'erreur quadratique moyenne varie entre 0.1 et 2m. La zone d'étude souffre d'un manque de données nécessaires pour élaborer la modélisation. Pour surmonter ce problème, nous avons eu recours aux mesures piézométriques effectuées par l'``UNDP'' dans des dizaines des puits de pompage dans la zone d'étude. Ces mesures sont utilisées dans un premier temps pour calibrer le flux d'eau douce entrant dans le domaine, puis pour valider le modèle expérimentalement. En plus, des compteurs volumétriques installés dans 38 puits de pompage ont montré que les habitants à Tripoli consomment la double quantité d'eau recommandée par le ministère des ressources en eau au Liban. Quatre scénarios de pompage basés sur le taux de croissance démographique, donné par le ministère des affaires sociales ont été étudiés. La hauteur de l'interface eau douce/eau salée associée à chaque scénario est calculée et comparée avec sa hauteur actuelle. Les résultats montrent que, avec la quantité d'eau pompée actuellement (250 litres par habitant par jour), la zone de pompage sera salinisée dans 20 ans, tandis que le respect des limites proposées par le ministère des ressources en eau (120 litres par habitant par jour) peut protéger l'aquifère à court terme. L'étude de scénario de croissance démographique est ensuite mise dans le contexte de changement climatique prédit dans le rapport du ``GIEC 2014'' pour la zone d'étude. Les évolutions pour les 25 prochaines années et pour trois phénomènes sont ainsi considérées: l'élévation du niveau de la mer, la variation du flux entrant d'eau douce et la variation du taux d'extraction d'eau douce de l'aquifère. La variation du flux entrant est imputée à la variation des régimes de précipitation dans les futures années. La variation de la couverture neigeuse est utilisée comme estimateur indirect pour la calibration du modèle. Le critère d'évaluation choisi est la position de la ligne de niveau 100m de l'interface eau douce/eau salée correspondant à la profondeur maximale des puits de pompage. L'étude montre que cette ligne avancera de 140m dans les 25 prochaines années. Les résultats montrent que l'impact de l'élévation du niveau de la mer (<1%) est très petit en comparaison avec celui de la variation de recharge (45%) et celui du taux d'extraction (54%). / The ground water resources represent 95% of the fresh water available in the world. ``UNEP'' reports predict that, 75% of people will live in coastal cities in 2020. These two informations show that coastal aquifers are essential in the elaboration of a water management strategy. Nowadays, coastal aquifers are subject to an over-exploitation that is leading to the aggravation of seawater intrusion phenomenon. Thus seawater intrusion modelling is necessary to assess and forecast the salinization of coastal aquifers. This work concerns the seawater intrusion modelling in Tripoli aquifer, Lebanon. Tripoli city lies on the Mediterranean coast and is home to one eighth of the Lebanese population (600,000). In this study, a mathematical model of sea water intrusion in Tripoli aquifer has been developed, based on the implementation of the sharp interface approximation in ``Freefem++''. This model provides primarily the depth of the freshwater/saltwater interface. The limitations of the model are exposed and the model is validated against analytic solution, against the numerical code ``BFSWIM'' and against terrain measurements where the root mean square error varies between 0.1 and 2m. The study zone suffers from scarceness of data necessary to elaborate the model. To overcome this problem, we use the piezometric measurements performed by the ``UNDP'' in tens of private wells in the studied zone. At first, we use these measurements to calibrate the flux of freshwater entering in the domain, then to validate experimentally the model. In addition, volumetric meters that have installed in $38$ buildings showed that water consumption through well extraction exceeds the recommendation of the Lebanese ministry of Energy and Water, which is 120 liters per capita per day. Four scenarios of pump basing on demographic growth rate given by the ministry of social affairs have been studied. Seawater intrusion height associated to each scenario has been calculated, then compared with its actual height. The results show that with this pumping rate (250 liters per capita per day), the pumping zone will be salinized within 20 years, while the respect of limitation proposed by the ministry of water resources and Energy can protect the aquifer for short time. This study of demographic growth scenario is then combined with the context of climate change predicted by ``IPCC2014'' and research studies in the region. Assessment of seawater intrusion for the 25 next years has been done, based on the following three phenomena: sea water rise, variation of fresh water flux entering in the domain and variation of freshwater extraction rate from the wells in the aquifer. The variation of snow cover is used as an indirect estimator to calibrate the model. The isocline 100m of saltwater/freshwater interface, which represents the maximal depth of pumping well, has been chosen as a criterion of evolution. Our study shows that this line will move forward about 140 m in the next 25 years leading to the salinization of the aquifer at the position of the pumping wells. The contribution of each parameter is assessed. We estimate that the sea water rise will contribute to less than 1% of this advance while the rate of recharge decrease and the rate of freshwater extraction increase contribute to 45% and 54% respectively of the isocline advance.

L’objectif de cette thèse est d’appréhender la complexité des mécanismes biologiques de l’acupuncture afin de construire un modèle mathématique multi-échelle. Ce modèle est étudié théoriquement et numériquement. L’acupuncture est une des plus vielles pratiques de l’histoire de la médecine et une partie intégrante de la médecine traditionnelle chinoise. Dans sa pratique la plus classique, une ou plusieurs aiguilles sont placées à des endroits spécifiques, nommés points d’acupuncture. L’aiguille est ensuite manipulée en utilisant des mouvements de rotation et de translation de façon à stimuler le point d’acupuncture. Les effets cliniques de l’acupuncture pourraient être le résultat d’effet de cascades de réactions produites par les interactions entre l’hypoderme et les systèmes nerveux, endocrinien et immunitaire. Le travail présenté s’articule sur la modélisation de l’insertion d’une aiguille dans le tissu conjonctif de l’hypoderme. Un modèle d’écoulement en milieu poreux du liquide interstitiel de l’hypoderme a permis d’étudier numériquement les composantes de contrainte qui agissent sur les récepteurs à la surface des cellules du tissu et notamment des mastocytes.Un modèle mathématique de la réponse chimiotactique des mastocytes à une contrainte physique créée par le traitement d’acupuncture est développé. Ce modèle prend en compte les mécanismes de signalisation cellulaire. La contrainte physique induit la libération rapide et continue, grâce au recrutement chimotactique de mastocytes, d’attractants et de médiateurs chimiques. Le modèle est basé sur le modèle de chimiotaxie de type Keller-Segel. / The objective of this thesis is to comprehend the complexity of the underlying basis of acupuncture. Acupuncture needling is investigated in order to establish a multiscale model that takes into account the complexity of biology but is mathematically simple enough to run simulations.Acupuncture is one of the oldest practices in the history of medicine and is the core of Traditional Chinese Medicine. Once needles are inserted in the right locations, called acupoints, they are manipulated via manual needling to stimulate the acupoint. The physiological reactions of acupuncture needling lead to therapeutic effects which can be explained by a series of interactions between the skin and the nervous, the endocrine, and the immune systems.In the present work, the thrusting and lifting of an acupuncture needle inserted in subcutaneous connective tissue is modeled. A porous media model is used to run simulations and compute the pressure and shear stress affecting the organization of fibers and of isolated cells in their matrix. A mathematical model was conceived to take into account cell signaling. There is ample evidence that needle manipulation in acupuncture can cause degranulation of mastocytes directly through a physical stress to occur. Activated mastocytes rapidly release granules containing chemical mediators. These chemical mediators play a key role recruiting mastocytes in their environment and are known to affect the excitability of nerve endings as well as local microcirculation permeability and size for the appropriate transfer of long-term acting endocrine signals. The process is sustained by the recruitment of mastocytes through chemotaxis.

Face au changement climatique global, il est de plus en plus important de prêter attention à la performance thermique-hydro-mécanique des constructions géotechniques sous l'effet des conditions atmosphériques. L'objectif principal de cette étude est d'étudier le comportement hydro-thermique des sols soumis au effets du changement climatique par la modélisation numérique.Un modèle hydro-thermique couplé est tout d'abord développé pour décrire le comportement du sol hydro-thermique. La théorie utilisée pour décrire l'interaction sol-atmosphère est présentée sous forme des bilans de masse et d'énergie. Ensuite, une approche numérique pour analyser le comportement hydro-thermique du sol est proposée en combinant le modèle hydro-thermique couplé avec un modèle d'interaction sol-atmosphère. La validation de cette approche est réalisée par la comparaison entre les résultats numériques obtenus en utilisant le code FreeFem++ et les données des essais de la colonne de séchage qui sont trouvées dans la littérature. Cette approche est d'abord utilisée pour la modélisation numérique des essais à la chambre environnementale, réalisés par Song en 2014. Des résultats de simulation satisfaisants sont obtenus en termes de variations de la température et de la teneur en eau volumétrique du sol. Ensuite, cette approche est appliquée à deux remblais, à Héricourt et à Rouen. Pour le remblai d’Héricourt, une étude numérique a été menée pour une durée de 20 jours. La bonne concordance obtenue entre les résultats de simulation et les mesures montre que l'approche proposée est pertinente pour l'analyse du comportement hydro-thermique du sol dans le cas de remblais bidimensionnels. Elle prouve également que les conditions aux limites et les paramètres du sol adoptés sont appropriés. Dans le cas du remblai de Rouen, deux périodes différentes, 187 jours et 387 jours, sont prises en considération. On vérifie également la bonne performance de l'approche proposée pour estimer le comportement hydro-thermique du remblai sous l'effet du climat. La comparaison entre les calculs et les mesures révèle également l'importance d'adopter correctement les conditions aux limites thermiques et hydrauliques ainsi que les paramètres du sol. De plus, à partir des simulations numériques, plusieurs suggestions sont faites pour collecter des données d'entrée dans l'application de cette approche pour prédire les variations de la température et de la teneur en eau du sol à plus long terme / Facing the global climate change, it is more and more important to pay attention to the thermal-hydro-mechanical performance of geotechnical constructions under the effect of atmospheric conditions. The main objective of this study is to investigate the hydro-thermal behavior of soil subjected to climate change through numerical modelling.A coupled hydro-thermal model is developed for describing the coupled hydro-thermal soil behavior. The soil-atmosphere interaction is studied through the mass and energy balances. Afterwards, a numerical approach to estimate soil hydro-thermal behavior by integrating the coupled hydro-thermal model with a soil-atmosphere interaction model is proposed. The validation of this approach is performed through the comparison between the numerical results using FreeFem++ code and the experimental data available from column drying tests reported in literature. This approach is firstly used for the numerical modelling of the environmental chamber tests carried out by Song in 2014. Satisfactory simulation results are obtained in terms of variations of soil temperature and soil volumetric water content. Afterwards, this approach is further applied to two cases of embankments, in Héricourt and in Rouen respectively. For Héricourt embankment, a numerical investigation was conducted for 20 days, and a good agreement between simulation results and filed measurements is obtained, showing that the proposed approach is suitable for analyzing the soil hydro-thermal behavior in the case of two-dimensional embankments. It proves also that the boundary conditions and the soil parameters adopted are appropriate. In the case of Rouen embankment, two different periods, 187 days and 387 days, are considered. The good performance of the proposed approach in estimating the embankment hydro-thermal behavior under the climate effect is also verified. The comparison between calculations and measurements also reveals the importance of appropriately adopting the thermal and hydraulic boundary conditions as well as the soil parameters. Based on the numerical simulations, several suggestions are made in terms of collection of input data for the application of this approach to predict soil temperature and volumetric water content variations in longer term

Les travaux de cette thèse concernent l'homogénéisation d'équations de Maxwell harmoniques tridimensionnelles, modélisant la propagation d'une onde électromagnétique issue de la foudre, de l'air dans le matériau composite. La problématique des composites étant, par exemple en aéronautique, l'évacuation de la foudre et la protection contre les agressions électromagnétiques. Nous considérons une structure constituée de fibres de carbone incluses dans une résine époxy qui sera elle-même nano chargée. Rendant ainsi le composite électriquement conducteur. Afin d'obtenir le problème homogénéisé nous utilisons l'analyse asymptotique à deux échelles. Puis nous justifions mathématiquement le résultat par la convergence à deux échelles. La solution du champ électrique est approchée par l'addition du champ électrique moyen et le champ correcteur, dépendant de la microstructure, et solution des problèmes de cellule. Dans la deuxième partie, nous proposons une validation numérique du modèle simplifié en 2D via des simulations avec le logiciel libre d'éléments finis Freefem ++. Trois cas tests seront présentés avant de valider la méthode d'homogénéisation. Enfin, en guise d'illustration du modèle, deux exemples d'agressions électromagnétiques : l'arc en retour de foudre de type A et une impulsion électromagnétique nucléaire seront testées dans le domaine fréquentiel. / The work of this thesis concerns the homogenization of three-dimensional harmonic Maxwell equations, modeling the propagation of an electromagnetic wave originating from lightning, from air in the composite material. The problem of composites being, for example in aeronautics, the evacuation of the lightning and the protection against the electromagnetic aggressions. We consider a structure made of carbon fibers included in an epoxy resin which will itself be nano- charged. Thus rendering the composite electrically conductive. In order to obtain the homogenized problem, we use asymptotic analysis at two scales. Then we mathematically justify the result by two-scale convergence. The solution of the electric field is approximated by the addition of the average electric field and the correct field, depending on the microstructure, and solution of the cell problems. In the second part, we propose a numerical validation of the simplified model in 2D via simulations with the free finite element software Freefem ++. Three test cases will be presented before validating the homogenization method. Finally, as an illustration of the model, two examples of electromagnetic aggression: the Type A lightning bolt and a nuclear electromagnetic pulse will be tested in the frequency domain.

Increasing environmental concerns as well as diminishing fossil fuel reserves call for a new generation of energy conversion technologies. Fuel cells, which convert the chemical energy of a fuel directly to electrical energy, have been identified as one of the leading alternative energy conversion technologies. Fuel cells are more efficient than conventional heat engines with minimal pollutant emissions and superior scalability. Proton Exchange Membrane Fuel Cells (PEMFCs) which produce electricity from hydrogen have been widely investigated for transportation and stationary applications. The focus of this study is on the Direct Propane Fuel Cell (DPFC), which belongs to the PEMFC family, but consumes propane instead of hydrogen as feedstock. A drawback associated with DPFCs is that the propane reaction rate is much slower than that of hydrogen. Two ideas were suggested to overcome this issue: (i) operating at high temperatures (150-230oC), and (ii) keeping the propane partial pressure at the maximum possible value. An electrolyte material composed of zirconium phosphate (ZrP) and polytetrafluoroethylene (PTFE) was suggested because it is an acceptable proton conductor at high temperatures. In order to keep the propane partial pressure at the maximum value, interdigitated flow-fields were chosen to distribute propane through the anode catalyst layer. In order to evaluate the performance of a DPFC which operates at high temperature and uses interdigitated flow-fields, a computational approach was chosen. Computational Fluid Dynamics (CFD) was used to create two 2-D mathematical models for DPFCs based on differential conservation equations. Two different approaches were investigated to model species transport in the electrolyte phase of the anode and cathode catalyst layers and the membrane layer. In the first approach, the migration phenomenon was assumed to be the only mechanism of proton transport. However, both migration and diffusion phenomena were considered as mechanisms of species transport in the second approach. Therefore, Ohm's law was used in the first approach and concentrated solution theory (Generalized Stefan-Maxwell equations) was used for the second one. Both models are isothermal. The models were solved numerically by implementing the partial differential equations and the boundary conditions in FreeFEM++ software which is based on Finite Element Methods. Programming in the C++ language was performed and the existing library of C++ classes and tools in FreeFEM++ were used. The final model contained 60 pages of original code, written specifically for this thesis. The models were used to predict the performance of a DPFC with different operating conditions and equipment design parameters. The results showed that using a specific combination of interdigitated flow-fields, ZrP-PTFE electrolyte having a proton conductivity of 0.05 S/cm, and operating at 230oC and 1 atm produced a performance (polarization curve) that was (a) far superior to anything in the DPFC published literature, and (b) competitive with the performance of direct methanol fuel cells. In addition, it was equivalent to that of hydrogen fuel cells at low current densities (30 mA/cm2).