Academic literature on the topic 'Discrete duality finite volumes'
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Journal articles on the topic "Discrete duality finite volumes"
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ANDREIANOV, B., M. BENDAHMANE, and K. H. KARLSEN. "DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS." Journal of Hyperbolic Differential Equations 07, no. 01 (March 2010): 1–67. http://dx.doi.org/10.1142/s0219891610002062.
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We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the construction and analysis of discrete duality finite volume schemes (in the spirit of Domelevo and Omnès [43]) for these problems in two and three spatial dimensions. We derive a series of discrete duality formulas and entropy dissipation inequalities for the schemes. We establish the existence of solutions to the discrete problems, and prove that sequences of approximate solutions generated by the discrete duality finite volume schemes converge strongly to the entropy solution of the continuous problem. The proof revolves around basic a priori estimates, the discrete duality features, Minty–Browder type arguments, and "hyperbolic" L∞weak-⋆ compactness arguments (i.e. propagation of compactness along the lines of Tartar, DiPerna, …). Our results cover the case of non-Lipschitz nonlinearities.
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Coudière, Yves, and Gianmarco Manzini. "The Discrete Duality Finite Volume Method for Convection-diffusion Problems." SIAM Journal on Numerical Analysis 47, no. 6 (January 2010): 4163–92. http://dx.doi.org/10.1137/080731219.
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Handlovicova, Angela. "Stability estimates for Discrete duality finite volume scheme of Heston model." Computer Methods in Material Science 17, no. 2 (2017): 101–10. http://dx.doi.org/10.7494/cmms.2017.2.0596.
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Tensor diffusion equation represents an important model in many fields of science. We focused our attention to the problem which arises in financial mathematics and is known as 2D Heston model. Stability estimates for discrete duality finite volume scheme for proposed model is presented. Numerical experiments using proposed method and comparing it with previous numerical scheme are included
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Tomek, Lukáš, and Karol Mikula. "Discrete duality finite volume method with tangential redistribution of points for surfaces evolving by mean curvature." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 6 (October 18, 2019): 1797–840. http://dx.doi.org/10.1051/m2an/2019040.
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We propose a new discrete duality finite volume method for solving mean curvature flow of surfaces in ℝ3. In the cotangent scheme, which is widely used discretization of Laplace–Beltrami operator, a two-dimensional surface is usually approximated by a triangular mesh. In the cotangent scheme the unknowns are the vertices of the triangulation. A finite volume around each vertex is constructed as a surface patch bounded by a piecewise linear curve with nodes in the midpoints of the neighbouring edges and a representative point of each adjacent triangle. The basic idea of our new approach is to include the representative points into the numerical scheme as supplementary unknowns and generalize discrete duality finite volume method from ℝ2 to 2D surfaces embedded in ℝ3. To improve the quality of the mesh we use an area-oriented tangential redistribution of the grid points. We derive the numerical scheme for both closed surfaces and surfaces with boundary, and present numerical experiments. Surface evolution models are applied to construction of minimal surfaces with given set of boundary curves.
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Chainais-Hillairet, C., S. Krell, and A. Mouton. "Study of Discrete Duality Finite Volume Schemes for the Peaceman Model." SIAM Journal on Scientific Computing 35, no. 6 (January 2013): A2928—A2952. http://dx.doi.org/10.1137/130910555.
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Coudière, Yves, and Florence Hubert. "A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations." SIAM Journal on Scientific Computing 33, no. 4 (January 2011): 1739–64. http://dx.doi.org/10.1137/100786046.
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Handlovičová, Angela, and Dana Kotorová. "Stability of the Semi-Implicit Discrete Duality Finite Volume Scheme for the Curvature Driven Level Set Equation in 2D." Tatra Mountains Mathematical Publications 61, no. 1 (December 1, 2014): 117–29. http://dx.doi.org/10.2478/tmmp-2014-0031.
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Abstract Stability of the linear semi-implicit discrete duality finite volume (DDFV) numerical scheme for the solution of the regularized curvature driven level set equation is proved. Our scheme is linear, it is efficient regarding computational times. Numerical experiments confirm accuracy of the proposed scheme
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Andreianov, Boris, Mostafa Bendahmane, and Florence Hubert. "On 3D DDFV Discretization of Gradient and Divergence Operators: Discrete Functional Analysis Tools and Applications to Degenerate Parabolic Problems." Computational Methods in Applied Mathematics 13, no. 4 (October 1, 2013): 369–410. http://dx.doi.org/10.1515/cmam-2013-0011.
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Abstract. We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete W1,p compactness, discrete compactness in space and in time) for the so-called Discrete Duality Finite Volume (DDFV) schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [IMA J. Numer. Anal., 32 (2012), pp. 1574–1603]. Some of our results are new, such as a general time-compactness result based upon the idea of Kruzhkov (1969); others generalize the ideas known for the 2D DDFV schemes or for traditional two-point-flux finite volume schemes. We illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray–Lions kind, and provide numerical results for this example.
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Njifenjou, Abdou, Abel Toudna Mansou, and Moussa Sali. "A New Second-order Maximum-principle-preserving Finite-volume Method for Flow Problems Involving Discontinuous Coefficients." American Journal of Applied Mathematics 12, no. 4 (August 26, 2024): 91–110. http://dx.doi.org/10.11648/j.ajam.20241204.12.
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A new development of Finite Volumes (FV, for short) and its theoretical analysis are the purpose of this work. Recall that FV are known as powerful tools to address equations of conservation laws (mass, energy, momentum,...). Over the last two decades investigators have succeeded in putting in place a mathematical framework for the theoretical analysis of FV. A perfect illustration of this progress is the design and mathematical analysis of Discrete Duality Finite Volumes (DDFV, for short). We propose now a new class of DDFV for 2nd order elliptic equations involving discontinuous diffusion coefficients or nonlinearities. A one-dimensional linear elliptic equation is addressed here for illustrating the ideas behind our numerical strategy. The algebraic structure of the discrete system we have got is different from that of standard DDFV. The main novelty is that the so-called diamond mesh elements are confined in homogeneous zones for flow problems governed by piecewise constant coefficients. This is got from our judicious definition of the primal mesh. The gain is that there is no need to compute homogenized coefficients to be allocated to the so-called diamond cells as required to conventional DDFV. Notice that poor homogenized permeability allocated to diamond elements leads to poor approximations of fluxes across grid-block interfaces. Moreover for 1-D flow problems in a porous medium involving permeability discontinuities (piecewise constant permeability for instance) the proposed FV scheme leads to a symmetric positive-definite discrete system that meets the discrete maximum principle; we have shown its second order convergence under relevant assumptions.
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Andreianov, Boris, Mostafa Bendahmane, Kenneth H. Karlsen, and Charles Pierre. "Convergence of discrete duality finite volume schemes for the cardiac bidomain model." Networks & Heterogeneous Media 6, no. 2 (2011): 195–240. http://dx.doi.org/10.3934/nhm.2011.6.195.
Full textDissertations / Theses on the topic "Discrete duality finite volumes"
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Paragot, Paul. "Analyse numérique du système d'équations Poisson-Nernst Planck pour étudier la propagation d'un signal transitoire dans les neurones." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5020.
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Les questions neuroscientifiques concernant les dendrites incluent la compréhension de leur plasticité structurale en réponse à l'apprentissage et la manière dont elles intègrent les signaux. Les chercheurs visent à élucider ces aspects pour améliorer notre compréhension de la fonction neuronale et de ses complexités. Cette thèse vise à offrir des perspectives numériques concernant la dynamique du voltage et des ions dans les dendrites. Notre objectif est de modéliser l'excitation neuronale dans les dendrites. Nous abordons la dynamique ionique suite à l'afflux de signaux nerveux. Pour les simuler précisément, nous résolvons le système d'équations Poisson-Nernst-Planck (PNP). Le système PNP est reconnu comme le modèle standard pour caractériser le phénomène d'électrodiffusion des ions dans les électrolytes, y compris les structures dendritiques. Ce système non linéaire présente des défis en modélisation et en calcul en raison de la présence de couches limites rigides (BL). Nous proposons des schémas numériques basés sur la méthode des volumes finis Discrete Duality Finite Volumes (DDFV) pour résoudre le système PNP. Elle permet un raffinement local du maillage au niveau de la BL, en utilisant des maillages généraux. Cette approche facilite la résolution du système sur un domaine 2D représentant la géométrie des dendrites. Nous utilisons des schémas numériques préservant la positivité des concentrations ioniques. Chapitres 1 et 2 présentent le système PNP et la méthode DDFV ainsi que ses opérateurs discrets. Le chapitre 2 présente un couplage "linéaire" des équations et explore son schéma numérique associé. Ce couplage a des problèmes de convergence, où nous illustrons ses limites à travers des résultats numériques. Le chapitre 3 introduit un couplage "non linéaire", permettant une résolution numérique précise du système PNP. Les deux couplages sont effectués avec la méthode DDFV. Dans le chapitre 3, nous illustrons la convergence d'ordre 2 en espace. Nous simulons un cas test impliquant la BL. Nous appliquons le schéma DDFV à la géométrie des épines dendritiques en 2D et discutons nos simulations en les comparant avec des simulations en 1D de la littérature. Nous introduisons également deux configurations originales de dendrites, fournissant des informations sur la manière dont les épines dendritiques s'influencent mutuellement, révélant l'étendue de leur influence mutuelle. Nos simulations montrent la distance de propagation de l'influx ionique lors des connexions synaptiques. Dans le chapitre 4, nous résolvons le système PNP sur un système multi-domaines 2D composé d'une membrane, d'un milieu interne et d'un milieu externe. Cette approche permet la modélisation de la dynamique du voltage de manière plus réaliste, et aide également à vérifier la cohérence des résultats du chapitre 3. Nous utilisons le logiciel FreeFem++ pour résoudre le système PNP dans ce contexte. Nous présentons des simulations correspondant aux résultats du chapitre 3, démontrant la sommation linéaire dans une bifurcation dendritique. Nous étudions la sommation des signaux en ajoutant des entrées à la membrane d'une branche dendritique. Nous identifions un seuil d'excitabilité où la dynamique du voltage est significativement influencée par le nombre d'entrées. Nous offrons également des illustrations numériques de la BL à l'intérieur du milieu intracellulaire, observant de petites fluctuations. Ces résultats sont préliminaires, visant à fournir des informations pour comprendre la dynamique dendritique. Le chapitre 5 présente un travail collaboratif mené lors du Cemracs 2022. Nous nous concentrons sur un schéma de volumes finis composite où nous visons à dériver les équations d'Euler avec des termes sources sur des maillages non structurésNeuroscientific questions about dendrites include understanding their structural plasticityin response to learning and how they integrate signals. Researchers aim to unravel these aspects to enhance our understanding of neural function and its complexities. This thesis aims at offering numerical insights concerning voltage and ionic dynamics in dendrites. Our primary focus is on modeling neuronal excitation, particularly in dendritic small compartments. We address ionic dynamics following the influx of nerve signals from synapses, including dendritic spines. To accurately represent their small scale, we solve the well-known Poisson-Nernst-Planck (PNP) system of equations, within this real application. The PNP system is widely recognized as the standard model for characterizing the electrodiffusion phenomenon of ions in electrolytes, including dendritic structures. This non-linear system presents challenges in both modeling and computation due to the presence of stiff boundary layers (BL). We begin by proposing numerical schemes based on the Discrete Duality Finite Volumes method (DDFV) to solve the PNP system. This method enables local mesh refinement at the BL, using general meshes. This approach facilitates solving the system on a 2D domain that represents the geometry of dendritic arborization. Additionally, we employ numerical schemes that preserve the positivity of ionic concentrations. Chapters 1 and 2 present the PNP system and the DDFV method along with its discrete operators. Chapter 2 presents a "linear" coupling of equations and investigate its associated numerical scheme. This coupling poses convergence challenges, where we demonstrate its limitations through numerical results. Chapter 3 introduces a "nonlinear" coupling, which enables accurate numerical resolution of the PNP system. Both of couplings are performed using DDFV method. However, in Chapter 3, we demonstrate the accuracy of the DDFV scheme, achieving second-order accuracy in space. Furthermore, we simulate a test case involving the BL. Finally, we apply the DDFV scheme to the geometry of dendritic spines and discuss our numerical simulations by comparing them with 1D existing simulations in the literature. Our approach considers the complexities of 2D dendritic structures. We also introduce two original configurations of dendrites, providing insights into how dendritic spines influence each other, revealing the extent of their mutual influence. Our simulations show the propagation distance of ionic influx during synaptic connections. In Chapter 4, we solve the PNP system over a 2D multi-domain consisting of a membrane, an internal and external medium. This approach allows the modeling of voltage dynamics in a more realistic way, and further helps checking consistency of the results in Chapter 3. To achieve this, we employ the FreeFem++ software to solve the PNP system within this 2D context. We present simulations that correspond to the results obtained in Chapter 3, demonstrating linear summation in a dendrite bifurcation. Furthermore, we investigate signal summation by adding inputs to the membrane of a dendritic branch. We identify an excitability threshold where the voltage dynamics are significantly influenced by the number of inputs. Finally, we also offer numerical illustrations of the BL within the intracellular medium, observing small fluctuations. These results are preliminary, aiming to provide insights into understanding dendritic dynamics. Chapter 5 presents collaborative work conducted during the Cemracs 2022. We focus on a composite finite volume scheme where we aim to derive the Euler equations with source terms on unstructured meshes
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Lakhlili, Jalal. "Modélisation et simulation numériques de l'érosion par méthode DDFV." Thesis, Toulon, 2015. http://www.theses.fr/2015TOUL0013/document.
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L’objectif de cette étude est de simuler l’érosion d’un sol cohésif sous l’effet d’un écoulement incompressible. Le modèle élaboré décrit une vitesse d’érosion interfaciale qui dépend de la contrainte de cisaillement de l’écoulement. La modélisation numérique proposée est une approche eulérienne, où une méthode de pénalisation de domaines est utilisée pour résoudre les équations de Navier-Stokes autour d’un obstacle. L’interface eau/sol est décrite par une fonction Level Set couplée à une loi d’érosion à seuil.L’approximation numérique est basée sur un schéma DDFV (Discrete Duality Finite Volume) autorisant des raffinements locaux sur maillages non-conformes et non-structurés. L’approche par pénalisation a mis en évidence une couche limite d'inconsistance à l'interface fluide/solide lors du calcul de la contrainte de cisaillement. Deux approches sont proposées pour estimer précisément la contrainte de ce problème à frontière libre. La pertinence du modèle à prédire l’érosion interfaciale du sol est confirmée par la présentation de plusieurs résultats de simulation, qui offrent une meilleure évaluation et compréhension des phénomènes d'érosionThis study focuses on the numerical modelling of the interfacial erosion occurring at a cohesive soil undergoing an incompressible flow process. The model assumes that the erosion velocity is driven by a fluid shear stress at the water/soil interface. The numerical modelling is based on the eulerian approach: a penalization procedure is used to compute Navier-Stokes equations around soil obstacle, with a fictitious domain method, in order to avoid body- fitted unstructured meshes. The water/soil interface’s evolution is described by a Level Set function coupled to a threshold erosion law.Because we use adaptive mesh refinement, we develop a Discrete Duality Finite Volume scheme (DDFV), which allows non-conforming and non-structured meshes. The penalization method, used to take into account a free velocity in the soil with non-body-fitted mesh, introduces an inaccurate shear stress at the interface. We propose two approaches to compute accurately the erosion velocity of this free boundary problem. The ability of the model to predict the interfacial erosion of soils is confirmed by presenting several simulations that provide better evaluation and comprehension of erosion phenomena
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Delcourte, Sarah. "DEVELOPPEMENT DE METHODES DE VOLUMES FINIS POUR LA MECANIQUE DES FLUIDES." Phd thesis, Université Paul Sabatier - Toulouse III, 2007. http://tel.archives-ouvertes.fr/tel-00200833.
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Le but de cette thèse est de développer une méthode de volumes finis qui s'applique à une classe de maillages beaucoup plus grande que celle des méthodes classiques, limitées par des conditions d'orthogonalité très restrictives. On construit des opérateurs différentiels discrets agissant sur les trois maillages décalés nécessaires à la construction de la méthode. Ces opérateurs vérifient des propriétés discrètes analogues à celles des opérateurs continus. La méthode est tout d'abord appliquée au problème divergence-rotationnel qui peut etre considéré comme une brique du problème de Stokes. Ensuite, le problème de Stokes est discrétisé avec diverses conditions aux limites. Par ailleurs, il est bien connu que lorsque le domaine est polygonal et non-convexe, l'ordre de convergence des méthodes numériques se dégrade. Par conséquent, nous avons étudié sous quelles conditions un raffinement local approprié permet de restaurer l'ordre de convergence optimal. Enfin, nous avons discrétisé le problème non-linéaire de Navier-Stokes, en utilisant la formulation rotationnelle du terme de convection, associée à la pression de Bernoulli. Par un algorithme itératif, nous sommes amenés à résoudre un problème de point-selle à chaque itération, pour lequel nous testons quelques préconditionneurs issus des éléments finis, que l'on adapte (quand c'est possible) à la méthode. Chaque problème est illustré par des cas tests numériques sur des maillages "arbitraires", tels que des maillages fortement non-conformes.
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Delcourte, Sarah. "Développement de méthodes de volumes finis pour la mécanique des fluides." Toulouse 3, 2007. http://thesesups.ups-tlse.fr/124/.
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Le but de cette thèse est de développer une méthode de volumes finis qui s'applique à une classe de maillages beaucoup plus grande que celle des méthodes classiques, limitées par des conditions d'orthogonalité très restrictives. On construit des opérateurs différentiels discrets agissant sur les trois maillages décalés, nécessaires à la construction de la méthode. Ces opérateurs vérifient des propriétés discrètes analogues à celles des opérateurs continus. La méthode est tout d'abord appliquées au problème Divergence-Rotationnel qui peut être considéré comme une brique du problème de Stokes. Ensuite, le problème de Stokes est traité avec diverses conditions aux limites. Par ailleurs, il est bien connu que lorsque le domaine est polygonal et non-convexe, l'ordre de convergence des méthodes numériques se dégrade. Par conséquent, nous avons étudié dans quelle mesure un raffinement local approprié restaure l'ordre de convergence optimal pour le problème de Laplace. Enfin, nous avons discrétisé le problème non-linéaire de Navier-Stokes, en utilisant la formulation rotationnelle du terme de convection, associé à la pression de Bernoulli. Par un algorithme itératif, nous sommes amené à résoudre un problème de point--selle à chaque itération, pour lequel nous testons quelques préconditionneurs issus des éléments finis, que l'on adapte à notre méthode. Chaque problème est illustré par des cas tests numériques sur des maillages arbitraires, tels que des maillages fortement non-conformesWe aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tesselations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriored. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle--point problem at each iteration. We give a particular interest to this linear problem by testing some preconditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes
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Omnes, Pascal. "Développement et analyse de méthodes de volumes finis." Habilitation à diriger des recherches, Université Paris-Nord - Paris XIII, 2010. http://tel.archives-ouvertes.fr/tel-00613239.
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Ce document synthétise un ensemble de travaux portant sur le développement et l'analyse de méthodes de volumes finis utilisées pour l'approximation numérique d'équations aux dérivées partielles issues de la physique. Le mémoire aborde dans sa première partie des schémas colocalisés de type Godunov d'une part pour les équations de l'électromagnétisme, et d'autre part pour l'équation des ondes acoustiques, avec une étude portant sur la perte de précision de ce schéma à bas nombre de Mach. La deuxième partie est consacrée à la construction d'opérateurs différentiels discrets sur des maillages bidimensionnels relativement quelconques, en particulier très déformés ou encore non-conformes, et à leur utilisation pour la discrétisation d'équations aux dérivées partielles modélisant des phénomènes de diffusion, d'électrostatique et de magnétostatique et d'électromagnétisme par des schémas de type volumes finis en dualité discrète (DDFV) sur maillages décalés. La troisième partie aborde ensuite l'analyse numérique et les estimations d'erreur a priori et a posteriori associées à la discrétisation par le schéma DDFV de l'équation de Laplace. La quatrième et dernière partie est consacrée à la question de l'ordre de convergence en norme $L^2$ de la solution numérique du problème de Laplace, issue d'une discrétisation volumes finis en dimension un et en dimension deux sur des maillages présentant des propriétés d'orthogonalité. L'étude met en évidence des conditions nécessaires et suffisantes relatives à la géométrie des maillages et à la régularité des données du problème afin d'obtenir la convergence à l'ordre deux de la méthode.
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Monasse, Laurent. "Analysis of a discrete element method and coupling with a compressible fluid flow method." Phd thesis, Université Paris-Est, 2011. http://pastel.archives-ouvertes.fr/pastel-00672342.
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This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an undeformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi-implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method
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Kunhappan, Deepak. "Modélisation numérique de l’écoulement de suspensions de fibres souples en régime inertiel." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAI045/document.
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Un modèle numérique décrivant le comportement de fibres souples en suspension dans un écoulement de fluide en régime inertiel a été développé au moyen d'un couplage entre la méthode des éléments discrets et la méthode des volumes finis. Chaque fibre est discrétisée en plusieurs éléments de type poutre permettant de prendre en compte une déformation (flexion, torsion, allongement) et un mouvement de corps rigide. Les équations du mouvement des fibres sont résolues au moyen d'un schéma explicite du second ordre (temps et espace). Le mouvement de la phase fluide est décrit par les équations de Navier-Stokes, qui sont discrétisées et résolues au moyen d'un schéma aux volumes finis non structurés, d'ordre 4 (temps et espace). Le couplage entre la phase solide (discrète) et la phase fluide (continue) est obtenue par une pseudo méthode IBM (Immersed Boundary Method) dans laquelle l'effort hydrodynamique est calculé analytiquement. Plusieurs modèles de force hydrodynamique issus de la littérature sont analysés et leur validité ainsi que leurs limites sont identifiées. Pour des nombres de Reynolds (Re) correspondant au régime inertiel (0.01 < Re < 100, Re défini à l'échelle de la fibre), des formulations non-linéaires de la force hydrodynamique exercée par un écoulement uniforme sur un cylindre infini sont utilisées. Le couplage a aussi été utilisé pour des fibres rigides en écoulement de Stokes, en utilisant l'expression de la force de traînée issue de la théorie des corps élancés (`slender body theory'). Une expression du moment hydrodynamique par unité de longueur est obtenu à partir de simulations numériques par volumes finis de l'écoulement autour d'un cylindre élancé.Le modèle développé a été validé par comparaison avec plusieurs résultats expérimentaux et analytiques, du régime de Stokes (pour des fibres rigides) jusqu'aux régimes inertiels. Dans le cas du régime de Stokes, des simulations numériques du cisaillement de suspensions de fibres semi-diluées ont été réalisées. Le modèle développé permet de capturer les interactions hydrodynamiques et non-hydrodynamiques entre les fibres. Les interactions élasto-hydrodynamiques pour $Re$ fini ont été validées dans deux cas. Dans le premier cas, la flèche d'une fibre encastrée-libre dans un écoulement uniforme a été obtenu par calcul numérique et le résultat validé par comparaison aux résultats expérimentaux de la littérature. Dans le second cas, la conformation de fibres élancées et très déformables dans un écoulement turbulent homogène et isotrope a été obtenu par calcul numérique et le résultat validé par comparaison aux résultats expérimentaux de la littérature. Deux études numériques ont été réalisées pour étudier l'effet de la présence de fibres en suspension sur la turbulence au sein du fluide suspensif. Le modèle numérique a permis de reproduire le phénomène de réduction/amplification de la turbulence dans un écoulement en canal ou en conduite, dû à l'évolution microstructurale de la phase fibreuseA numerical model describing the behavior of flexible fibers under inertial flows was developed by coupling a discrete element solver with a finite volume solver.Each fiber is discretized into several beam segments, such that the fiber can bend, twist and rotate. The equations of the fiber motion were solved usinga second order accurate explicit scheme (space and time). The three dimensional Navier-Stokes equations describing the motion of the fluid phase was discretizedusing a fourth th order accurate (space and time) unstructured finite volume scheme. The coupling between the discrete fiber phase and the continuous fluid phasewas obtained by a pseudo immersed boundary method as the hydrodynamic force on the fiber segments were calculated based on analytical expressions.Several hydrodynamic force models were analyzed and their validity and short-comings were identified. For Reynolds numbers (Re) at the inertial regime(0.01 < Re < 100, Re defined at the fiber scale), non linear drag force formulations based on the flow past an infinite cylinder was used. For rigid fibers in creeping flow, the drag force formulation from the slender body theory was used. A per unit length hydrodynamic torque model for the fibers was derived from explicit numerical simulations of shear flow past a high aspect ratio cylinder. The developed model was validated against several experimental studies and analytical theories ranging from the creeping flow regime (for rigid fibers) to inertial regimes. In the creeping flow regime, numerical simulations of semi dilute rigid fiber suspensions in shear were performed.The developed model wasable to capture the fiber-fiber hydrodynamic and non-hydrodynamic interactions. The elasto-hydrodynamic interactions at finite Reynolds was validated with against two test cases. In the first test case, the deflection of the free end of a fiber in an uniform flow field was obtained numerically and the results were validated. In the second test case the conformation of long flexible fibers in homogeneous isotropic turbulence was obtained numerically and the results were compared with previous experiments. Two numerical studies were performed to verify the effects of the suspended fibers on carrier phase turbulence and the numerical model was able to reproduce the damping/enhancement phenomena of turbulence in channel and pipe flows as a consequence of the micro-structural evolution of the fibers
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Catalano, Emanuele. "Modélisation physique et numérique de la micro-mécanique des milieux granulaires saturés. Application à la stabilité de substrats sédimentaires en génie cotier." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENU012/document.
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Le comportement des matériaux multiphasiques couvre une multitude de phénomènes qui suscitent un grand intérêt dans le domaine scientifique et professionnel. Les propriétés mécaniques de ces types de matériau trouvent leur origine dans les phases dont ils sont composés, leur distribution et interaction. Un nouveau modèle hydrodynamique couplé est présenté dans ce travail de thèse, à appliquer à l'analyse de l'hydrodynamique des milieux granulaires saturés. Le modèle associe la méthode des éléments discrets (DEM) pour la modélisation de la phase solide, avec une formulation en volumes finis, à l'échelle des pores (PFV), du problème de l'écoulement. Une importance particulière est donné à la description de l'interaction entre les phases, avec la détermination des forces fluides à appliquer sur chacune des particule, tout en assurant un coût de calcul abordable, qui permet la modélisation de plusieurs milliers des particules en trois dimensions. Le milieux est considéré saturé par un fluide incompressible. Les pores et leur connectivité est basée sur une triangulation régulière des assemblages. L'analogie de cette formulation avec la théorie classique de Biot est présenté. Le modèle est validé par la comparaison des résultats numériques obtenus pour un problème de consolidation d'un sol granulaire avec la solution analytique de Terzaghi. Une approche pour analyser l'hydrodynamique d'un sédiment granulaire est finalement présenté. La reproduction du phénomène de liquéfaction d'un sol est également présentéeThe behaviour of multiphase materials covers a wide range of phenomena of interest to both scientists and engineers. The mechanical properties of these materials originate from all component phases, their distribution and interaction. A new coupled hydromechanical model is presented in this work, to be applied to the analysis of the hydrodynamics of saturated granular media. The model associates the discrete element method (DEM) for the solid phase, and a pore-scale finite volume (PFV) formulation of the flow problem. The emphasis of this model is, on one hand, the microscopic description of the interaction between phases, with the determination of the forces applied on solid particles by the fluid; on the other hand, the model involve affordable computational costs, that allow the simulation of thousands of particles in three dimensional models. The medium is assumed to be saturated of an incompressible fluid. Pore bodies and their connections are defined locally through a regular triangulation of the packings. The analogy of the DEM-PFV model and the classic Biot's theory of poroelasticity is discussed. The model is validated through comparison of the numerical result of a soil consolidation problem with the Terzaghi's analytical solution. An approach to analyze the hydrodynamic of a granular sediment is finally presented. The reproduction of the phenomenon of soil liquefaction is analysed and discussed
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Bessemoulin-Chatard, Marianne. "Développement et analyse de schémas volumes finis motivés par la présentation de comportements asymptotiques. Application à des modèles issus de la physique et de la biologie." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2012. http://tel.archives-ouvertes.fr/tel-00836514.
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Cette thèse est dédiée au développement et à l'analyse de schémas numériques de type volumes finis pour des équations de convection-diffusion, qui apparaissent notamment dans des modèles issus de la physique ou de la biologie. Nous nous intéressons plus particulièrement à la préservation de comportements asymptotiques au niveau discret. Ce travail s'articule en trois parties, composées chacune de deux chapitres. Dans la première partie, nous considérons la discrétisation du système de dérive diffusion linéaire pour les semi-conducteurs par le schéma de Scharfetter-Gummel implicite en temps. Nous nous intéressons à la préservation par ce schéma de deux types d'asymptotiques : l'asymptotique en temps long et la limite quasi-neutre. Nous démontrons des estimations d'énergie-dissipation d'énergie discrètes qui permettent de prouver d'une part la convergence en temps long de la solution approchée vers une approximation de l'équilibre thermique, d'autre part la stabilité à la limite quasi-neutre du schéma. Dans la deuxième partie, nous nous intéressons à des schémas volumes finis préservant l'asymptotique en temps long dans un cadre plus général. Plus précisément, nous considérons des équations de type convection-diffusion non linéaires qui apparaissent dans plusieurs contextes physiques : équations des milieux poreux, système de dérive-diffusion pour les semi-conducteurs... Nous proposons deux discrétisations en espace permettant de préserver le comportement en temps long des solutions approchées. Dans un premier temps, nous étendons la définition du flux de Scharfetter-Gummel pour une diffusion non linéaire. Ce schéma fournit des résultats numériques satisfaisants si la diffusion ne dégénère pas. Dans un second temps, nous proposons une discrétisation dans laquelle nous prenons en compte ensemble les termes de convection et de diffusion, en réécrivant le flux sous la forme d'un flux d'advection. Le flux numérique est défini de telle sorte que les états d'équilibre soient préservés, et nous utilisons une méthode de limiteurs de pente pour obtenir un schéma précis à l'ordre deux en espace, même dans le cas dégénéré. Enfin, la troisième et dernière partie est consacrée à l'étude d'un schéma numérique pour un modèle de chimiotactisme avec diffusion croisée pour lequel les solutions n'explosent pas en temps fini, quelles que soient les données initiales. L'étude de la convergence du schéma repose sur une estimation d'entropie discrète nécessitant l'utilisation de versions discrètes d'inégalités fonctionnelles telles que les inégalités de Poincaré-Sobolev et de Gagliardo-Nirenberg-Sobolev. La démonstration de ces inégalités fait l'objet d'un chapitre indépendant dans lequel nous proposons leur étude dans un contexte assez général, incluant notamment le cas de conditions aux limites mixtes et une généralisation au cadre des schémas DDFV.
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Nguyen-Dinh, Maxime. "Qualification des simulations numériques par adaptation anisotropique de maillages." Phd thesis, Université Nice Sophia Antipolis, 2014. http://tel.archives-ouvertes.fr/tel-00987202.
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La simulation numérique est largement utilisée pour évaluer les performances aérodynamiques des aéronefs ainsi qu'en optimisation de forme. Ainsi l'objectif de ces simulations est souvent le calcul de fonctions aérodynamiques. L'objet de cette thèse est d'étudier des méthodes d'adaptation de maillages basées sur la dérivée totale de ces fonctions par rapport aux coordonnées du maillage (notée dJ/dX). Celle-ci pouvant être calculée par la méthode adjointe discrète. La première partie de cette étude concerne l'application de méthodes d'adaptation de maillages appliquées à des écoulements de fluides parfaits. Le senseur qui détecte les zones de maillage à raffiner s'appuie sur la norme de cette dérivée pour adapter des maillages pour le calcul d'une fonction J. La seconde partie du travail est la construction et l'étude de critères plus fiables basés sur dJ/dX pour d'une part adapter des maillages et d'autre part estimer si un maillage est bien adapté ou non pour le calcul de la fonction J. De plus une méthode de remaillage plus efficace basée sur une EDP elliptique est aussi présentée. Cette nouvelle méthode est appliquée pour des écoulements bidimensionnels de fluides parfaits ainsi que pour un écoulement décrit par les équations RANS. La dernière partie de l'étude est consacrée à l'application de la méthode proposée à des cas tridimensionnels d'écoulement RANS sur des géométries d'intérêt industriel.
Book chapters on the topic "Discrete duality finite volumes"
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Martin, Benjamin, and Frédéric Pascal. "Discrete Duality Finite Volume Method Applied to Linear Elasticity." In Finite Volumes for Complex Applications VI Problems & Perspectives, 663–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_70.
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Boyer, Franck, Stella Krell, and Flore Nabet. "Benchmark Session: The 2D Discrete Duality Finite Volume Method." In Springer Proceedings in Mathematics & Statistics, 163–80. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57397-7_11.
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Coudière, Yves, and Charles Pierre. "Benchmark 3D: CeVe-DDFV, a Discrete Duality Scheme with Cell/Vertex Unknowns." In Finite Volumes for Complex Applications VI Problems & Perspectives, 1043–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_102.
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Coudière, Yves, Florence Hubert, and Gianmarco Manzini. "Benchmark 3D: CeVeFE-DDFV, a discrete duality scheme with cell/vertex/face+edge unknowns." In Finite Volumes for Complex Applications VI Problems & Perspectives, 977–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_95.
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Handlovičová, Angela, and Peter Frolkovič. "Semi-implicit Alternating Discrete Duality Finite Volume Scheme for Curvature Driven Level Set Equation." In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 333–42. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05684-5_32.
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Cancès, Clément, Claire Chainais-Hillairet, and Stella Krell. "A Nonlinear Discrete Duality Finite Volume Scheme for Convection-Diffusion Equations." In Springer Proceedings in Mathematics & Statistics, 439–47. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57397-7_37.
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Delcourte, Sarah, and Pascal Omnes. "Numerical Results for a Discrete Duality Finite Volume Discretization Applied to the Navier–Stokes Equations." In Springer Proceedings in Mathematics & Statistics, 141–61. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57397-7_10.
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Enock, Michel, and Jean-Marie Schwartz. "Special Cases: Unimodular, Compact, Discrete and Finite-Dimensional Kac Algebras." In Kac Algebras and Duality of Locally Compact Groups, 192–241. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02813-1_7.
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Glitzky, Annegret, and Jens A. Griepentrog. "On Discrete Sobolev–Poincaré Inequalitiesfor Voronoi Finite Volume Approximations." In Finite Volumes for Complex Applications VI Problems & Perspectives, 533–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_56.
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Gallouët, Thierry, David Maltese, and Antonín Novotný. "Discrete Relative Entropy for the Compressible Stokes System." In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 383–92. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05684-5_37.
Full textConference papers on the topic "Discrete duality finite volumes"
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Geng, Yanlin, and Fan Cheng. "Duality between finite numbers of discrete multiple access and broadcast channels." In 2015 IEEE Information Theory Workshop - Fall (ITW). IEEE, 2015. http://dx.doi.org/10.1109/itwf.2015.7360755.
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Voulgaris, Petros. "Multi-Objecitve Control of Dynamical Systems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0345.
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Abstract In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.
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Xie, Yawei, and Michael G. Edwards. "Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids." In SPE Reservoir Simulation Conference. SPE, 2021. http://dx.doi.org/10.2118/203957-ms.
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Abstract A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.
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Wu, Dawei, Yuan Di, Zhijiang Kang, and Yu-Shu Wu. "Coupled Geomechanics and Fluid Flow Modeling for Petroleum Reservoirs Accounting for Multi-Scale Fractures." In SPE Reservoir Simulation Conference. SPE, 2023. http://dx.doi.org/10.2118/212247-ms.
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Abstract Accurate modeling of fractured reservoirs is very challenging due to the various scales of fractures. The fracture networks may be too complex to be represented using the equivalent continuum model (ECM) or dual porosity-dual permeability (DPDK) model, yet too computational costly to be modeled using the discrete fracture (DFM) or embedded discrete fracture (EDFM) models. This paper proposes a hybrid model that integrates ECM, DPDK, and an integrally embedded discrete fracture model (IEDFM) to account for multi-scale fractures. The hybrid model is applied to investigate the coupled geomechanics-fluid flow process in fractured reservoirs. In the hybrid model, small-scale fractures are upscaled into effective matrix permeability tensor using ECM, medium-scale fractures are considered as an individual continuum using DPDK, and large-scale fractures are explicitly represented using IEDFM. The multiphase flow in effective matrix and fracture continua is modeled using the multi-point flux approximation (MPFA), and fluid exchanges between the anisotropic continua and the large-scale fracture control volumes are precisely calculated using the IEDFM. Empirical models are used to calculate the displacement of natural fractures, and analytical models are used to calculate the aperture changes of hydraulic fractures. The overall deformation of a fractured rock is described using an equivalent method. The coupled geomechanics-fluid flow system is discretized by the finite element-finite volume method (FV-FEM) and solved using the fixed-stress split iterative coupling approach. Several examples are presented to demonstrate the applicability of the proposed method. The hybrid model is first employed to simulate water flooding process in a naturally fractured reservoir with multi-scale fractures. Effects of different scales of fractures, geomechanics coupling and capillary pressure are investigated. A case of producing from horizontal well in a hydraulic fractured tight oil reservoir is then studied, where the hydraulic fractures are modeled explicitly using IEDFM and the stimulation areas around hydraulic fractures are modeled using DPDK. Effects of stimulation area size on the pressure depletion and on the stress evolution process in the reservoir are investigated.
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Choi, Kwang Won, Dan Negrut, and Darryl G. Thelen. "GPU-Based Algorithm for Fast Computation of Cartilage Contact Patterns During Simulations of Movement." In ASME 2013 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/sbc2013-14095.
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Direct measurement of cartilage contact is not feasible, necessitating the use of musculoskeletal models to estimate the internal soft tissue loading associated with movement2. However, current computational models used to simulate movement often utilize simplified joint kinematic constraints which can only provide an estimate of the net joint reaction force1. Detailed finite element models of the knee have been created14 which can provide estimates of cartilage tissue stress, but are too computationally expensive to solve within the context of a whole body simulation of movement. Discrete element analysis (DEA) provides a viable alternative for rapidly computing contact stress patterns in movement15, However, even DEA models can be computationally expensive as high resolution polygonal meshes are needed to accurately represent complex cartilage geometries such as that seen on the femoral condyles and tibia plateau. In a DEA model, much of the computation time is spent querying for contact between triangles of two polygonal surfaces. The objective of this study was to investigate the potential for using graphic processor computation (GPU) to expedite contact detection5. To do this, we use a contact detection algorithm that pre-constructs hierarchical bounding-volumes (BVH) of the target body to increase the efficiency of contact detection. We then show that implementing a parallel computational version of this algorithm on the GPU greatly speed up performance and thus make it more viable to simulate cartilage contact within the context of human movement.
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Tong, Timothy W., Mohsen M. Abou-Ellail, Yuan Li, and Karam R. Beshay. "Numerical Prediction of Nitrogen Oxides in Radiant Porous Burner Flows." In ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference collocated with the ASME 2007 InterPACK Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ht2007-32064.
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The present paper is concerned with the numerical computation of flow, heat transfer and chemical reactions in porous burners. The porous solid matrix acts as a host for redistributing the thermal energy transferred to it from the hot reacting gases. Inside the porous matrix, heat is transferred down stream by conduction and radiation. This thermal energy is then transferred to the incoming cold fuel/air mixture to initiate the chemical reaction processes and thus stabilize the flame. One of the important features of porous burners is its presumed low levels of NO concentration. In the present work, the computed NOx is compared with experimental data and open premixed flames. In order to accurately compute the nitric oxide levels in porous burners, both prompt and thermal NOx mechanisms are included. In the present work, the porous burner species mass fraction source terms are computed from an ‘extended’ reaction mechanism, controlled by chemical kinetics of elementary reactions. The porous burner has mingled zones of porous/nonporous reacting flow, i.e., the porosity is not uniform over the entire domain. Finite-volume equations are obtained by formal integration over control volumes surrounding each grid node. Up-wind differencing is used to insure that the influence coefficients are always positive. Finite-difference equations are solved, iteratively, for velocity components, pressure correction, gas enthalpy, species mass fractions and solid matrix temperature. A non-uniform (80×80) computational grid is used. The grid used to solve the solid energy equation is extended inside the solid annular wall of the porous burner, to improve its modeling. A discrete-ordinate model with S4 quadrature is used for the computation of thermal radiation emitted from the solid matrix. The porous burner uses a premixed CH4-air mixture, while its radiating characteristics are required to be studied numerically under equivalence ratios 0.6 and 0.5. Twenty-five species are included, involving 75 elementary chemical reactions. The computed solid wall temperature profiles are compared with experimental data for similar porous burners. The obtained agreement is fairly good. Some reacting species, such as H2O, CO2, H2, NO and N2O increase steadily inside the reaction zone. However, unstable products, such as HO2, H2O2 and CH3, increase in the preheating zone to be depleted afterward.
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Gradl, Christoph, Ivo Kovacic, and Rudolf Scheidl. "Development of an Energy Saving Hydraulic Stepper Drive." In 8th FPNI Ph.D Symposium on Fluid Power. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fpni2014-7809.
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Stepper drives can realize quite precise, incremental motions without position sensors. Sensorless hydraulic motion control is strongly demanded by industry and, therefore, is an established idea in hydraulics for a while. Some concepts have been proposed in the past and a few of them have also been realized and applied in specific cases. But it is expected that digital hydraulics — due to its intrinsic discrete nature — can create new, more advantageous hydraulic versions of stepper drives. In this paper, a new stepper drive is presented and investigated. It creates the steps by fixed fluid quanta generated by a so called digital flow unit. That unit is realized by a hydraulic cylinder-piston unit which displaces a defined fluid quantum by each limited forward stroke of that piston. The unit is controlled by a fast switching valve which connects the piston areas alternately with the pressure-, tank- and output-line. The return motion is generated by a return spring. Energy saving is accomplished by storing the supply pressure surplus intermediately in the kinetic energy of the piston and converting that energy to displace part of the quantum to the consumer line without hydraulic energy from the supply line. Different detail concepts of this stepper drive are theoretically assessed. The transient behavior, the performance characteristics and the energy efficiency of a preferred concept are investigated by mathematical modeling and simulation. Furthermore, the main system parameters are identified and corresponding basic dimensioning rules are presented. In a second step, the influence of finite switching times of the valves, the hydraulic impedances of the various flow channels and of the dead volumes and the dynamical properties of the hydraulic cylinder attached to the device, are discussed.
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Tong, Timothy W., Mohsen M. Abou-Ellail, Yuan Li, and Karam R. Beshay. "Computation of Nitrogen Oxides in Radiant Porous Burner Flows." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56229.
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The present paper is concerned with the numerical computation of flow, heat transfer and chemical reactions in porous burners. One of the important features of porous burners is their presumed low levels of nitrogen oxides. In the present work, the computed NOx is compared with similar conventional premixed burners and measured nitrogen oxides in porous burners. In order to accurately compute the nitrogen oxides levels in porous burners, both prompt and thermal NOx mechanisms are included. In the present work, the porous burner species mass fraction source terms are computed from an ‘extended’ reaction mechanism, controlled by chemical kinetics of elementary reactions. The porous burner has mingled zones of porous/nonporous reacting flow, i.e. the porosity is not uniform over the entire domain. Finite-volume equations are obtained by formal integration over control volumes surrounding each grid node. Up-wind differencing is used to ensure that the influence coefficients are always positive to reflect the real effect of neighboring nodes on a typical central node. Finite-difference equations are solved iteratively for velocity components, pressure correction, gas enthalpy, species mass fractions and solid matrix temperature. The grid used to solve the solid energy equation is extended inside the zero-porosity solid annular wall of the burner porous disk. This was found useful for computing the solid wall temperature with high accuracy. A two-dimensional, discrete-ordinate, model is used for the computation of thermal radiation emitted from the solid matrix. The porous burner uses a premixed CH4-air mixture, while its radiating characteristics are studied numerically under equivalence ratio ranging from 0.5 to 0.8. Twenty-one species are included, involving 55 chemical reactions. The computed solid wall temperature profiles are compared with experimental data of similar porous burners. The obtained agreement is fairly good. The present numerical results show that as the equivalent ratio decreases, the reaction zone moves downstream. Moreover, as the flame speed increases, the NOx mole fraction increases. Some reacting species, such as H2O, CO2 and H2 increase steadily inside the reaction zone; they stay appreciable in the combustion products. However, unstable products, such as HO2, H2O2 and CH3, first increase in the preheating region of the reaction zone; they are then consumed in the remaining part of the reaction zone. The numerical results show that most of the formed NOx is composed of nitric oxide. The velocity and temperature profiles were accurately predicted using a grid of 80×80 while the nitrogen oxides were computed accurately utilizing a finer grid of 160×160.
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Cao, Wen, and Rami M. Younis. "Numerical Study of the Influences of Dynamic Loading and Unloading Rates on Fracturing." In 57th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2023. http://dx.doi.org/10.56952/arma-2023-0936.
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ABSTRACT Dynamic loading offers the potential to induce densely connected fractured pore space over large bulk volumes of impermeable rock. An understanding of the impacts of the dynamic loading and unloading rates on the resulting fracturing can guide the design of discharge technologies. This work numerically investigates the dependence of the extent of fracturing on dynamic loading characteristics. We reconcile a high-fidelity model (finite-discrete element method with nonlinear fracture mechanics) with experimental observations. The model is subsequently used to simulate various loading scenarios spanning laboratory to field scale conditions. INTRODUCTION In contrast to hydraulic fracturing, high-energy dynamic loads generate radial fractures which are not influenced by formation stress anisotropy. This removes the need for determining the in-situ stress orientation, which is a necessary factor in designing horizontal wells that undergo multiple hydraulic fracturing treatments. This study aims to investigate the effect of different dynamic load functions on seismic fracturing. One way to create high-energy dynamic loads is to use explosives (e.g., Grady et al. (Grady et al., 1980), Banadaki et al. (Banadaki, 2010), Zhang et al. (Zhang et al., 2017), and Jeong et al. (Jeong et al., 2020)). Explosives generate loading pulses with a maximum peak pressure that can exceed 1 GPa and a rise time of the pressure waveform on the order of 1 to 2 microseconds. Experiences using explosives are well-documented and span applications in various materials like granite, shale, and PMMA. The body of reported experiments shows that the extent of crack propagation depends on the energy released by the explosive charge, although a quantitative understanding of this relationship remains elusive for formations in the deep subsurface which cannot be observed directly or with great resolution. Another type of technology delivers the dynamic load using shock waves created in liquid. Hamelin et al. (Haimson and Fairhurst, 1967), Maurel et al. (Maurel et al., 2010), Chen et al. (Chen et al., 2012), and Xiao et al. (Xiao et al., 2018) for instance, applied Pulsed Arc Electrohydraulic Discharges (PAED) to produce shock waves in water. These loading profiles typically involve a longer time for the load to reach its peak. Moreover, in the case of laboratory experiments, reflections of shock waves from the finite samples may create extra fractures. To study the potential of formation fracturing at the field scale, large sample sizes, a wide variety of high energy loadings, and accurate diagnostics are needed. Given the challenge and costs of such extensive experimentation, numerical simulation can offer a useful alternative to narrow down the range of pulses to be investiated.