Dans ce travail de thèse, un aperçu général sur les systèmes PON est présenté et sont étudiés les mécanismes et classification PON existants. Après, nous introduisons notre première contribution qui est un algorithme d'allocation dynamique de bande passante pour EPON. Cet algorithme proposé est désigné comme «hcDBA». Par la suite, une amélioration de l'algorithme de hcDBA avec mécanisme de prédiction précoce est présentée. Notre simulation montre bien que notre algorithme hcDBA est performant comparé aux mécanismes existants en termes de taux de perte de paquets et de délai d’accès. Dans notre seconde contribution, nous sommes intéressés au problème de consommation d’énergie qui est un sujet d’actualité dans les réseaux de télécommunication. Les études montrent aujourd’hui que les réseaux d'accès constituent une partie remarquable de la consommation totale d'énergie dans les réseaux de télécommunication. Les organisations ITU-T et IEEE ont publié la recommandation pour la conversation de l'énergie pour les réseaux PONs. Bien que, la consommation totale d'énergie des nœuds ONU est plus importantes que d'autres équipements dans le réseau d'accès fixe, les normes et la plupart des travaux de recherches ont porté sur les économies d'énergie du côté de ONU. Dans cette thèse, nous sommes concentrés sur une méthode d'efficacité énergétique basée sur la conservation de l'énergie du côté de l’OLT. La méthode proposée permet d’économiser de l'énergie en déplaçant dynamiquement des cartes d’OLT en mode de sommeil profond en fonction des charges de trafic entrant et sortant / In this thesis, general overview about PON systems is presented and existing PON mechanisms and classification are investigated. After, a novel dynamic bandwidth allocation algorithm for EPON is introduced. This proposed algorithm is named as “Half Cycling Dynamic Bandwidth Allocation-hcDBA” by the inspiration of its half cycling processing mode. Later, an improvement of hcDBA algorithm with early prediction mechanism is presented. As a result statement of the study, hcDBA algorithm performs better than existing mechanism in terms of packet loss ratio and access delays. Beside, simulation traffic behavior of EPON’s upstream channel has been investigated in order to support the decision of selecting suitable traffic generator in further studies. Energy conversation is one of the hot topics in telecommunication networks. Access networks constitute remarkable portion of the total energy consumption in telecommunication networks. ITU-T and IEEE organizations published recommendation for energy conversation in PONs. While, total energy consumption of ONUs is more than other equipment in fix access network the standards and most of the researches focused on saving energy at ONU side. In this thesis I focused on an energy efficiency method based on energy conversation on OLT side. The proposed method save energy by dynamically moving OLT cards to deep sleep mode according to the incoming and outgoing traffic loads

L'interférence entre stations de base est considérée comme le principal facteur limitant les performances des réseaux cellulaires. Nous nous intéressons aux différents schémas de coordination multi-point (CoMP) proposés dans la norme LTE-A pour y faire face, en tenant compte de l'aspect dynamique du trafic et de la mobilité des utilisateurs. Les résultats sont obtenus par l'analyse mathématique de modèles markoviens et par des simulations du système. Nous montrons l'importance de l'algorithme d'ordonnancement sur les performances en présence d'utilisateurs mobiles, pour des services de téléchargement de fichier et de streaming vidéo. Nous proposons un nouvel algorithme d'ordonnancement basé sur la dé-priorisation des utilisateurs mobiles se trouvant en bord de cellule, afin d'améliorer l'efficacité globale du système. Nous montrons ensuite qu'il est intéressant d'activer la technique dite Joint Processing uniquement dans un réseau à forte interférence, son activation dans un réseau à faible interférence pouvant conduire à une dégradation des performances. Nous proposons un nouveau mécanisme de coordination où une cellule ne coopère que lorsque sa coopération apporte un gain moyen de débit suffisant pour compenser les pertes de ressources engendrées. Nous considérons enfin la technique de formation de faisceaux coordonnée. Nous montrons notamment que la coordination n'est pas nécessaire lorsque l'on dispose d'un grand nombre d'antennes par station de base, un simple mécanisme d'ordonnancement opportuniste permettant d'obtenir des performances optimales. Pour un nombre limité d’antennes parstation de base, la coordination est nécessaire afin d’éviter l’interférence entre les faisceaux activés, et permet des gains de performance substantiels. / Interference is still the main limiting factor in cellular networks. We focus on the different coordinated multi-point schemes (CoMP) proposed in the LTE-A standard to cope with interference, taking into account the dynamic aspect of traffic and users’ mobility. The results are obtained by the analysis of Markov models and system-level simulations. We show the important impact of the scheduling strategy on the network performance in the presence of mobile users considering elastic traffic and video streaming. We propose a new scheduler that deprioritizes mobile users at the cell edge, in order to improve the overall system efficiency. We show that it is interesting to activate Joint Processing technique only in a high-interference network, its activation in a low-interference network may lead to performance degradation. We propose a new coordination mechanism, where a cell cooperates only when its cooperation brings a sufficient mean throughput gain, which compensates the extra resource consumption. Finally, we show that the coordination of beams is not necessary when a large number of antennas is deployed at each base station; a simple opportunistic scheduling strategy provides optimal performance. For a limited number of antennas per base station,coordination is necessary to avoid interference between the activated beams, allowing substantial performance gains.

The next generation wireless networks i.e. 5G aim to provide multi-Gbps data traffic, in order to satisfy the increasing demand for high-definition video, among other high data rate services, as well as the exponential growth in mobile subscribers. To achieve this dramatic increase in data rates, current research is focused on improving the capacity of current 4G network standards, based on Long Term Evolution (LTE), before radical changes are exploited which could include acquiring additional/new spectrum. The LTE network has a reuse factor of one; hence neighbouring cells/sectors use the same spectrum, therefore making the cell edge users vulnerable to inter-cell interference. In addition, wireless transmission is commonly hindered by fading and pathloss. In this direction, this thesis focuses on improving the performance of cell edge users in LTE and LTE-Advanced (LTE-A) networks by initially implementing a new Coordinated Multi-Point (CoMP) algorithm to mitigate cell edge user interference. Subsequently Device-to-Device (D2D) communication is investigated as the enabling technology for maximising Resource Block (RB) utilisation in current 4G and emerging 5G networks. It is demonstrated that the application, as an extension to the above, of novel power control algorithms, to reduce the required D2D TX power, and multihop transmission for relaying D2D traffic, can further enhance network performance. To be able to develop the aforementioned technologies and evaluate the performance of new algorithms in emerging network scenarios, a beyond-the-state-of-the-art LTE system-level simulator (SLS) was implemented. The new simulator includes Multiple-Input Multiple-Output (MIMO) antenna functionalities, comprehensive channel models (such as Wireless World initiative New Radio II i.e. WINNER II) and adaptive modulation and coding schemes to accurately emulate the LTE and LTE-A network standards. Additionally, a novel interference modelling scheme using the 'wrap around' technique was proposed and implemented that maintained the topology of flat surfaced maps, allowing for use with cell planning tools while obtaining accurate and timely results in the SLS compared to the few existing platforms. For the proposed CoMP algorithm, the adaptive beamforming technique was employed to reduce interference on the cell edge UEs by applying Coordinated Scheduling (CoSH) between cooperating cells. Simulation results show up to 2-fold improvement in terms of throughput, and also shows SINR gain for the cell edge UEs in the cooperating cells. Furthermore, D2D communication underlaying the LTE network (and future generation of wireless networks) was investigated. The technology exploits the proximity of users in a network to achieve higher data rates with maximum RB utilisation (as the technology reuses the cellular RB simultaneously), while taking some load off the Evolved Node B (eNB) i.e. by direct communication between User Equipment (UE). Simulation results show that the proximity and transmission power of D2D transmission yields high performance gains for a D2D receiver, which was demonstrated to be better than that of cellular UEs with better channel conditions or in close proximity to the eNB in the network. The impact of interference from the simultaneous transmission however impedes the achievable data rates of cellular UEs in the network, especially at the cell edge. Thus, a power control algorithm was proposed to mitigate the impact of interference in the hybrid network (network consisting of both cellular and D2D UEs). It was implemented by setting a minimum SINR threshold so that the cellular UEs achieve a minimum performance, and equally a maximum SINR threshold to establish fairness for the D2D transmission as well. Simulation results show an increase in the cell edge throughput and notable improvement in the overall SINR distribution of UEs in the hybrid network. Additionally, multihop transmission for D2D UEs was investigated in the hybrid network: traditionally, the scheme is implemented to relay cellular traffic in a homogenous network. Contrary to most current studies where D2D UEs are employed to relay cellular traffic, the use of idle nodes to relay D2D traffic was implemented uniquely in this thesis. Simulation results show improvement in D2D receiver throughput with multihop transmission, which was significantly better than that of the same UEs performance with equivalent distance between the D2D pair when using single hop transmission.

Les surfaces tactiles ayant connu un grand essor ces dernières années, le grand public les utilise quotidiennement pour de multiples tâches, telles que la consultation d'e-mail, la manipulation de photos, etc. En revanche, très peu d'applications 3D existent sur ces dispositifs, alors que de telles applications pourraient avoir un grand potentiel dans des domaines variés, telles que la culture, l'architecture, ou encore l'archéologie. La difficulté majeure pour ce type d'applications est d'interagir avec un espace défini en trois dimensions à partir d'une modalité d'interaction définie en deux dimensions. Les travaux effectués dans cette thèse explorent l'association entre surfaces tactiles et manipulation de contenu 3D pour le grand public. Les premières études ont été réalisées afin de comprendre comment l'utilisateur réagit pour manipuler un objet virtuel 3D avec une surface tactile sans lui imposer de techniques d'interaction particulières. De par les connaissances acquises sur les utilisateurs, les travaux suivants présentent l'élaboration de nouvelles techniques d'interaction ainsi que leur évaluation. / Since the emergence of tactile surfaces in recent years, the general public uses them every day for multiple tasks, such as checking email, photo manipulation, and so on. However, very few 3D applications on these devices exist, although such applications may have great potential in various fields, such as culture, architecture, or archeology. The major difficulty for such applications is to interact with a defined space in three dimensions from an interaction modality defined in two dimensions. Work in this thesis explores the association between tactile surfaces and manipulation of 3D content for the general public. The first studies were conducted to understand how the user tends to manipulate a 3D virtual object with a touch surface without imposing specific interaction techniques. Throughout knowledge gained by users, the following works are developing new interaction techniques and their evaluation.

Le sujet de cette thèse est la conception et l'implantation d'algorithmes efficaces pour des opérations de base en calcul formel, ainsi que leurs applications à des domaines connexes, comme la théorie algorithmique des nombres et la cryptographie. Une première partie traite de l'algorithmique de base sur les polynômes à une variable. L'outil systématiquement mis en oeuvre est une version constructive du principe de transposition de Tellegen, qui permet d'obtenir de nouveaux algorithmes pour l'évaluation multipoint et l'interpolation (dans diverses bases polynomiales et pour diverses familles de points d'évaluation), ainsi qu'un théorème d'équivalence entre les complexités de ces deux problèmes. La deuxième partie est consacrée à l'algorithmique des nombres algébriques. Nous étudions d'abord certaines opérations élémentaires, comme la somme, le produit et leur généralisation, le produit diamant de Brawley et Carlitz. Leur calcul repose sur l'utilisation de l'opérateur de Newton formel et de la dualité algébrique, traduite algorithmiquement par l'emploi du principe de transposition et des méthodes de type pas de bébés / pas de géants. Ces méthodes sont ensuite généralisées au cadre des systèmes de polynômes de dimension zéro, pour le calcul de polynômes minimaux dans des algèbres quotient, ainsi que de paramétrisations rationnelles. Dans la troisième partie, nous étudions la question du calcul d'un terme d'une suite récurrente linéaire à coefficients polynomiaux. Comme application, nous obtenons des améliorations théoriques et pratiques des méthodes de comptage de points utilisées en cryptographie. Nous proposons ensuite une méthode de type évaluation-interpolation pour certaines opérations usuelles sur les opérateurs différentiels linéaires à coefficients polynomiaux.

No description available.

Este trabalho apresenta um sistema de conferência multiponto centralizada com controle de posse da palavra, que oferece comunicação por voz e por texto, desenvolvido para dar suporte a ferramentas de educação a distância baseadas em tecnologia web. Além do sistema de conferência multiponto, este trabalho introduz, também, conceitos de voz sobre IP (VoIP), codecs de áudio, tráfego de tempo real sobre redes IP, mecanismos de distribuição de pacotes em redes IP, conferências multimídia sobre redes IP, criação e controle de conferências e mecanismos para se controlar a transmissão de pacotes de voz em conferências multiponto, como detecção de atividade de voz (VAD) e controle de posse da palavra. O controle de posse da palavra ou moderação é uma metodologia para coordenar o acesso a recursos de mídia contínua, como os canais de áudio e vídeo em conferências, resolvendo eventuais conflitos e condições de corrida e garantindo o uso exclusivo dos mesmos por um participante da conferência. O controle de posse da palavra é apropriado para a dinâmica de uma sala de aula, onde na maioria das vezes, o professor exerce o papel de um moderador e de principal interlocutor. Além de regular o fluxo de informação na sala de aula virtual, o controle de posse da palavra também ajuda a reduzir a utilização dos recursos da rede. Como principal resultado deste trabalho, uma arquitetura para o sistema de conferência multiponto foi proposta, implementada e testada. Verificou-se que o sistema é escalável e que o controle de posse da palavra reduz o grau de interatividade entre os participantes da conferência, mas funciona eficazmente como mecanismo para reduzir a utilização dos recursos de rede. A comunicação adicional por texto ajuda a reduzir o impacto do controle de posse da palavra no grau de interatividade. Neste trabalho, o uso de uma topologia centralizada para a realização de conferências multiponto mostrou-se bastante vantajoso, principalmente porque o tráfego multicast não era suportado. / This work presents a centralized multipoint conference system with floor control, which offers voice and text communication capability, developed to support distance learning tools based on web technology. This work also brings concepts about voice over IP (VoIP), audio codecs, real-time traffic over IP networks, packet distribution mechanisms in IP networks, multimedia conferences over IP networks, establishment and control of conferences and mechanisms to control voice packets transmission in multipoint conferences, as Voice Activity Detection (VAD) and floor control. Floor control is a suitable methodology for coordinating access to continuous media resources, such as audio and video channels in conferences, solving resource conflicts and race conditions and guaranteeing their mutually exclusive use by one participant of the conference. Floor control is appropriate for the classroom’s dynamics, where the teacher, mostly, has the role of a moderator and main talker. Besides regulating the information flow in the virtual classroom, floor control helps reducing the need for network resources. As main result, an architecture for the multipoint conference system was proposed, implemented and tested. It was found that the system is scalable and that floor control reduces the interactivity among the conference’s participants, but works efficiently as a mechanism for reducing the need for network resources. Text communications help lowering the impact of floor control on interactivity. In this work, the deployment of a centralized topology for multipoint conferences showed to be very advantageous, mainly because multicast traffic was not supported.

Este trabalho apresenta um sistema de conferência multiponto centralizada com controle de posse da palavra, que oferece comunicação por voz e por texto, desenvolvido para dar suporte a ferramentas de educação a distância baseadas em tecnologia web. Além do sistema de conferência multiponto, este trabalho introduz, também, conceitos de voz sobre IP (VoIP), codecs de áudio, tráfego de tempo real sobre redes IP, mecanismos de distribuição de pacotes em redes IP, conferências multimídia sobre redes IP, criação e controle de conferências e mecanismos para se controlar a transmissão de pacotes de voz em conferências multiponto, como detecção de atividade de voz (VAD) e controle de posse da palavra. O controle de posse da palavra ou moderação é uma metodologia para coordenar o acesso a recursos de mídia contínua, como os canais de áudio e vídeo em conferências, resolvendo eventuais conflitos e condições de corrida e garantindo o uso exclusivo dos mesmos por um participante da conferência. O controle de posse da palavra é apropriado para a dinâmica de uma sala de aula, onde na maioria das vezes, o professor exerce o papel de um moderador e de principal interlocutor. Além de regular o fluxo de informação na sala de aula virtual, o controle de posse da palavra também ajuda a reduzir a utilização dos recursos da rede. Como principal resultado deste trabalho, uma arquitetura para o sistema de conferência multiponto foi proposta, implementada e testada. Verificou-se que o sistema é escalável e que o controle de posse da palavra reduz o grau de interatividade entre os participantes da conferência, mas funciona eficazmente como mecanismo para reduzir a utilização dos recursos de rede. A comunicação adicional por texto ajuda a reduzir o impacto do controle de posse da palavra no grau de interatividade. Neste trabalho, o uso de uma topologia centralizada para a realização de conferências multiponto mostrou-se bastante vantajoso, principalmente porque o tráfego multicast não era suportado. / This work presents a centralized multipoint conference system with floor control, which offers voice and text communication capability, developed to support distance learning tools based on web technology. This work also brings concepts about voice over IP (VoIP), audio codecs, real-time traffic over IP networks, packet distribution mechanisms in IP networks, multimedia conferences over IP networks, establishment and control of conferences and mechanisms to control voice packets transmission in multipoint conferences, as Voice Activity Detection (VAD) and floor control. Floor control is a suitable methodology for coordinating access to continuous media resources, such as audio and video channels in conferences, solving resource conflicts and race conditions and guaranteeing their mutually exclusive use by one participant of the conference. Floor control is appropriate for the classroom’s dynamics, where the teacher, mostly, has the role of a moderator and main talker. Besides regulating the information flow in the virtual classroom, floor control helps reducing the need for network resources. As main result, an architecture for the multipoint conference system was proposed, implemented and tested. It was found that the system is scalable and that floor control reduces the interactivity among the conference’s participants, but works efficiently as a mechanism for reducing the need for network resources. Text communications help lowering the impact of floor control on interactivity. In this work, the deployment of a centralized topology for multipoint conferences showed to be very advantageous, mainly because multicast traffic was not supported.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-01T15:05:14Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Souza_Tese_2015_09_22.pdf: 8187999 bytes, checksum: 664629aed28d692dce410fefbfe793dc (MD5) / Made available in DSpace on 2016-07-01T15:05:14Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Souza_Tese_2015_09_22.pdf: 8187999 bytes, checksum: 664629aed28d692dce410fefbfe793dc (MD5) Previous issue date: 2015-09-22 / Anp / Sob certas hipóteses simplificadoras, o modelo matemático que descreve o escoamento de água e óleo em reservatórios de petróleo pode ser representado por um sistema não linear de Equações Diferenciais Parciais composto por uma equação elíptica de pressão (fluxo) e uma equação hiperbólica de saturação (transporte). Devido a complexidades na modelagem de ambientes deposicionais, nos quais são incluídos camadas inclinadas, canais, falhas e poços inclinados, há uma dificuldade de se construir um modelo que represente adequadamente certas características dos reservatórios, especialmente quando malhas estruturadas são usadas (cartesianas ou corner point). Além disso, a modelagem do escoamento multifásico nessas estruturas geológicas incluem descontinuidades na variável e instabilidades no escoamento, associadas à elevadas razões de mobilidade e efeitos de orientação de malha. Isso representa um grande desafio do ponto de vista numérico. No presente trabalho, uma formulação fundamentada no Método de Volumes Finitos é estudada e proposta para discretizar as equações elíptica de pressão e hiperbólica de saturação. Para resolver a equação de pressão três formulações robustas, com aproximação dos fluxos por múltiplos pontos são estudadas. Essas formulações são abeis para lidar com tensores de permeabilidade completos e malhas poligonais arbitrárias, sendo portanto uma generalização de métodos mais tradicionais com aproximação do fluxo por apenas dois pontos. A discretização da equação de saturação é feita com duas abordagens com característica multidimensional. Em uma abordagem mais convencional, os fluxos numéricos são extrapolados diretamente nas superfícies de controle por uma aproximação de alta resolução no espaço (2ª a 4ª ordem) usando uma estratégia do tipo MUSCL. Uma estratégia baseada na Técnica de Mínimos Quadrados é usada para a reconstrução polinomial. Em uma segunda abordagem, uma variação de uma esquema numérico Verdadeiramente Multidimensional é proposto. Esse esquema diminui o efeito de orientação de malha, especialmente para malhas ortogonais, mesmo embora alguma falta de robustez possa ser observada pra malhas excessivamente distorcidas. Nesse tipo de formulação, os fluxos numéricos são calculados de uma forma multidimensional. Consiste em uma combinação convexa de valores de saturação ou fluxo fracionário, seguindo a orientação do escoamento através do domínio computacional. No entanto, a maioria dos esquemas numéricos achados na literatura tem aproximação apenas de primeira ordem no espaço e requer uma solução implícita de sistemas algébricos locais. Adicionalmente, no presente texto, uma forma modificada desses esquemas “Verdadeiramente” Multidimensionais é proposta em um contexto centrado na célula. Nesse caso, os fluxos numéricos multidimensionais são calculados explicitamente usando aproximações de alta ordem no espaço. Para o esquema proposto, a robustez e o caráter multidimensional também leva em conta a distorção da malha por meio de uma ponderação adaptativa. Essa ponderação regula a característica multidimensional da formulação de acordo com a distorção da malha. Claramente, os efeitos de orientação de malha são reduzidos. A supressão de oscilações espúrias, típicas de aproximações de alta ordem, são obtidas usando, pela primeira vez no contexto de simulação de reservatórios, uma estratégia de limitação multidimensional ou Multidimensional Limiting Process (MLP). Essa estratégia garante soluções monótonas e podem ser usadas em qualquer malha poligonal, sendo naturalmente aplicada em aproximações de ordem arbitrária. Por fim, de modo a garantir soluções convergentes, mesmo para problemas tipicamente não convexos, associados ao modelo de Buckley-Leverett, uma estratégia robusta de correção de entropia é empregada. O desempenho dessas formulações é verificado com a solução de problemas relevantes achados na literatura. / Under certain simplifying assumptions, the problem that describes the fluid flow of oil and water in heterogeneous and anisotropic petroleum reservoir can be described by a system of non-linear partial differential equations that comprises an elliptic pressure equation (flow) and a hyperbolic saturation equation (transport). Due to the modeling of complex depositional environments, including inclined laminated layers, channels, fractures, faults and the geometrical modeling of deviated wells, it is difficult to properly build and handle the Reservoir Characterization Process (RCM), particularly by using structured meshes (cartesian or corner point), which is the current standard in petroleum reservoir simulators. Besides, the multiphase flow in such geological structures includes the proper modeling of water saturation shocks and flow instabilities associated to high mobility ratios and Grid Orientation Effects (GOE), posing a great challenge from a numerical point of view. In this work, a Full Finite Volume Formulation is studied and proposed to discretize both, the elliptic pressure and the hyperbolic saturation equations. To solve the pressure equation, we study and use three robust Multipoint Flux Approximation Methods (MPFA) that are able to deal with full permeability tensors and arbitrary polygonal meshes, making it relatively easy to handle complex geological structures, inclined wells and mesh adaptivity in a natural way. To discretize the saturation equation, two different multidimensional approaches are employed. In a more conventional approach, the numerical fluxes are extrapolated directly on the control surfaces for a higher resolution approximation in space (2nd to 4th order) by a MUSCL (Monotone Upstream Centered Scheme for Conservation Laws) procedure. A least squares based strategy is employed for the polynomial reconstruction. In a second approach, a variation of a “Truly” Multidimensional Finite Volume method is proposed. This scheme diminishes GOE, especially for orthogonal grids, even though some lack of robustness can be observed for extremely distorted meshes. In this type of scheme, the numerical flux is computed in each control surface in a multidimensional way, by a convex combination of the saturation or the fractional flow values, following the approximate wave orientation throughout the computational domain. However, the majority of the schemes found in literature is only first order accurate in space and demand the implicit solution of local conservation problems. In the present text, a Modified Truly Multidimensional Finite Volume Method (MTM-FVM) is proposed in a cell centered context. The truly multidimensional numerical fluxes are explicitly computed using higher order accuracy in space. For the proposed scheme, the robustness and the multidimensional character of the aforementioned MTM-FVM explicitly takes into account the angular distortion of the computational mesh by means of an adaptive weight, that tunes the multidimensional character of the formulation according to the grid distortion, clearly diminishing GOE. The suppression of the spurious oscillations, typical from higher order schemes, is achieved by using for the first time in the context of reservoir simulation a Multidimensional Limiting Process (MLP). The MLP strategy formally guarantees monotone solutions and can be used with any polygonal mesh and arbitrary orders of approximation. Finally, in order to guarantee physically meaningful solutions, a robust “entropy fix” strategy is employed. This produces convergent solutions even for the typical non-convex flux functions that are associated to the Buckley-Leverett problem. The performance of the proposed full finite volume formulation is verified by solving some relevant benchmark problems.