Academic literature on the topic 'Hybrid Cartesian/unstructured meshes'
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Journal articles on the topic "Hybrid Cartesian/unstructured meshes"
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Gansen, A., M. El Hachemi, S. Belouettar, O. Hassan, and K. Morgan. "A 3D Unstructured Mesh FDTD Scheme for EM Modelling." Archives of Computational Methods in Engineering 28, no. 1 (January 17, 2020): 181–213. http://dx.doi.org/10.1007/s11831-019-09395-z.
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AbstractThe Yee finite difference time domain (FDTD) algorithm is widely used in computational electromagnetics because of its simplicity, low computational costs and divergence free nature. The standard method uses a pair of staggered orthogonal cartesian meshes. However, accuracy losses result when it is used for modelling electromagnetic interactions with objects of arbitrary shape, because of the staircased representation of curved interfaces. For the solution of such problems, we generalise the approach and adopt an unstructured mesh FDTD method. This co-volume method is based upon the use of a Delaunay primal mesh and its high quality Voronoi dual. Computational efficiency is improved by employing a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of curved interfaces and hexahedral elements elsewhere. Difficulties associated with ensuring the necessary quality of the generated meshes will be discussed. The power of the proposed solution approach is demonstrated by considering a range of scattering and/or transmission problems involving perfect electric conductors and isotropic lossy, anisotropic lossy and isotropic frequency dependent chiral materials.
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Busto, Saray, Michael Dumbser, and Laura Río-Martín. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows." Mathematics 9, no. 22 (November 21, 2021): 2972. http://dx.doi.org/10.3390/math9222972.
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This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.
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Hoagland, Dylan S., and Yousry Y. Azmy. "PARAMETRIC STUDY OF PARALLEL BLOCK JACOBI / SOURCE ITERATION HYBRID METHODS IN 2-D CARTESIAN GEOMETRY AND CONSTRUCTION OF THE INTEGRAL TRANSPORT MATRIX METHOD MATRICES VIA GREEN’S FUNCTIONS." EPJ Web of Conferences 247 (2021): 03017. http://dx.doi.org/10.1051/epjconf/202124703017.
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Parallel Block Jacobi (PBJ) [1] is an asynchronous spatial domain decomposition with application in solving the neutron transport equation due to its extendibility to massively parallel solution in unstructured spatial meshes (grids) without the use of the computationally complex and expensive sweeps required by the Source Iteration (SI) method in these applications. [2] However, PBJ iterative methods suffer a lack of iterative robustness in problems with optically thin cells, [1] which we have previously demonstrated to be a consequence of PBJ’s asynchronicity. To mitigate this effect, we have developed multiple PBJ / SI hybrid methods which employ a PBJ method (Parallel Block Jacobi - Integral Transport Matrix Method (PBJ-ITMM) or Inexact Parallel Block Jacobi (IPBJ)) along with SI. [3,4] In this work, we perform a parametric study to determine performance of numerous PBJ / SI hybrid methods as a function of multiple problem parameters. This parametric study reached 5 main conclusions: 1) our hybrid approach is more effective with PBJ-ITMM than with IPBJ, 2) for PBJ-ITMM, there is a hybrid method that mitigates the aforementioned iterative slowdown in optically thin cells without diminishing the method’s potential parallelism in unstructured grids, 3) this hybrid method is most effective in problems with large, continuous regions of very thin cells, 4) the best performing hybrid method consistently executes within a factor of ten slower than current state-of-the-art acceleration methods that are not efficiently extendable to the massively parallel regime, and 5) both PBJ-ITMM and IPBJ are observed to be viable approaches for our desired applications. In the pursuit of implementing PBJ-ITMM in unstructured grids, we conclude with a description of the Green’s Function ITMM Construction (GFIC) algorithm, which allows for the ITMM matrices to be constructed using the pre-existing SI sweep algorithm already present in unstructured grid SN transport codes.
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Zhang, Yang, and Chunhua Zhou. "Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method." Advances in Applied Mathematics and Mechanics 8, no. 1 (December 21, 2015): 145–65. http://dx.doi.org/10.4208/aamm.2014.m590.
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AbstractIn this work, the hybrid solution reconstruction formulation proposed by Luo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries, Computers & Fluids, 56 (2012), pp. 61–76] for the finite-difference discretization on Cartesian meshes is implemented in the finite-element framework of the local domain-free discretization (DFD) method to reduce the numerical oscillations in the simulation of moving-boundary flows. The reconstruction formulation is applied at fluid nodes in the immediate vicinity of the immersed boundary, which combines weightly the local DFD solution with the specific values obtained via an approximation of quadratic polynomial in the normal direction to the wall. The quadratic approximation is associated with the no-slip boundary condition and the local simplified momentum equation. The weighted factor suitable for unstructured triangular and tetrahedral meshes is constructed, which is related to the local mesh intervals near the immersed boundary and the distances from exterior dependent nodes to the boundary. Therefore, the reconstructed solution can account for the smooth movement of the immersed boundary. Several numerical experiments have been conducted for two- and three-dimensional moving-boundary flows. It is shown that the hybrid reconstruction approach can work well in the finite-element context and effectively reduce the numerical oscillations with little additional computational cost, and the spatial accuracy of the original local DFD method can also be preserved.
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Rüger, Andreas, and Dave Hale. "Meshing for velocity modeling and ray tracing in complex velocity fields." GEOPHYSICS 71, no. 1 (January 2006): U1—U11. http://dx.doi.org/10.1190/1.2159061.
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In seismic processing, velocity fields are commonly represented on finely sampled Cartesian grids. Attractive alternatives are unstructured grids such as meshes composed of triangles or tetrahedra. Meshes provide a space-filling framework that enables editing of velocity models while facilitating numerical tasks such as seismic modeling and inversion. In this paper, we introduce an automated process to generate meshes of subsurface velocity structures for highly resolved velocity fields without providing additional external constraints such as horizons and faults. Our analysis shows that these new meshes can represent both smooth and discontinuous velocity profiles accurately and with less computer memory than grids.
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Wei, Ran, Futing Bao, Yang Liu, and Weihua Hui. "Robust Three-Dimensional Level-Set Method for Evolving Fronts on Complex Unstructured Meshes." Mathematical Problems in Engineering 2018 (September 25, 2018): 1–15. http://dx.doi.org/10.1155/2018/2730829.
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With a purpose to evolve the surfaces of complex geometries in their normal direction at arbitrarily defined velocities, we have developed a robust level-set approach which runs on three-dimensional unstructured meshes. The approach is built on the basis of an innovative spatial discretization and corresponding gradient-estimating approach. The numerical consistency of the estimating method is mathematically proven. A correction technology is utilized to improve accuracy near sharp geometric features. Validation tests show that the proposed approach is able to accurately handle geometries containing sharp features, computation regions having irregular shapes, discontinuous speed fields, and topological changes. Results of the test problems fit well with the reference results produced by analytical or other numerical methods and converge to reference results as the meshes refine. Compared to level-set method implementations on Cartesian meshes, the proposed approach makes it easier to describe jump boundary conditions and to perform coupling simulations.
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Fridrich, David, Richard Liska, Ivan Tarant, Pavel Váchal, and Burton Wendroff. "CELL-CENTERED LAGRANGIAN LAX-WENDROFF HLL HYBRID SCHEME ON UNSTRUCTURED MESHES." Acta Polytechnica 61, SI (February 10, 2021): 68–76. http://dx.doi.org/10.14311/ap.2021.61.0068.
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We have recently introduced a new cell-centered Lax-Wendroff HLL hybrid scheme for Lagrangian hydrodynamics [Fridrich et al. J. Comp. Phys. 326 (2016) 878-892] with results presented only on logical rectangular quadrilateral meshes. In this study we present an improved version on unstructured meshes, including uniform triangular and hexagonal meshes and non-uniform triangular and polygonal meshes. The performance of the scheme is verified on Noh and Sedov problems and its second-order convergence is verified on a smooth expansion test.Finally the choice of the scalar parameter controlling the amount of added artificial dissipation is studied.
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Skamarock, William C., Joseph B. Klemp, Michael G. Duda, Laura D. Fowler, Sang-Hun Park, and Todd D. Ringler. "A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering." Monthly Weather Review 140, no. 9 (September 1, 2012): 3090–105. http://dx.doi.org/10.1175/mwr-d-11-00215.1.
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Abstract The formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as accurate as existing nonhydrostatic solvers for nonhydrostatic-scale flows, and has accuracy comparable to existing global models using icosahedral (hexagonal) meshes for large-scale flows in idealized tests. Preliminary full-physics forecast results indicate that the solver formulation is robust and that the variable-resolution-mesh solutions are well resolved and exhibit no obvious problems in the mesh-transition zones.
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Ahuja, Vineet, Ashvin Hosangadi, and Srinivasan Arunajatesan. "Simulations of Cavitating Flows Using Hybrid Unstructured Meshes." Journal of Fluids Engineering 123, no. 2 (January 29, 2001): 331–40. http://dx.doi.org/10.1115/1.1362671.
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A new multi-phase model for low speed gas/liquid mixtures is presented; it does not require ad-hoc closure models for the variation of mixture density with pressure and yields thermodynamically correct acoustic propagation for multi-phase mixtures. The solution procedure has an interface-capturing scheme that incorporates an additional scalar transport equation for the gas void fraction. Cavitation is modeled via a finite rate source term that initiates phase change when liquid pressure drops below its saturation value. The numerical procedure has been implemented within a multi-element unstructured framework CRUNCH that permits the grid to be locally refined in the interface region. The solution technique incorporates a parallel, domain decomposition strategy for efficient 3D computations. Detailed results are presented for sheet cavitation over a cylindrical head form and a NACA 66 hydrofoil.
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Mut, Fernando, Gustavo C. Buscaglia, and Enzo A. Dari. "New Mass-Conserving Algorithm for Level Set Redistancing on Unstructured Meshes." Journal of Applied Mechanics 73, no. 6 (February 1, 2006): 1011–16. http://dx.doi.org/10.1115/1.2198244.
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The level set method is becoming increasingly popular for the simulation of several problems that involve interfaces. The level set function is advected by some velocity field, with the zero-level set of the function defining the position of the interface. The advection distorts the initial shape of the level set function, which needs to be re-initialized to a smooth function preserving the position of the zero-level set. Many algorithms re-initialize the level set function to (some approximation of) the signed distance from the interface. Efficient algorithms for level set redistancing on Cartesian meshes have become available over the last years, but unstructured meshes have received little attention. This presentation concerns algorithms for construction of a distance function from the zero-level set, in such a way that mass is conserved on arbitrary unstructured meshes. The algorithm is consistent with the hyperbolic character of the distance equation (‖∇d‖=1) and can be localized on a narrow band close to the interface, saving computing effort. The mass-correction step is weighted according to local mass differences, an improvement over usual global rebalancing techniques.
Dissertations / Theses on the topic "Hybrid Cartesian/unstructured meshes"
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Simmons, Daniel. "Hybrid methods for modelling advanced electromagnetic systems using unstructured meshes." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33230/.
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The aim of this project is the conception, implementation, and application of a simulation tool for the accurate modeling of electromagnetic fields within inhomogeneous materials with complex shapes and the propagation of the resulting fields in the surrounding environment. There are many methods that can be used to model the scattering of an electromagnetic field, however one of the most promising for hybridisation is the Boundary Element Method (BEM), which is a surface technique, and the Unstructured Transmission Line Modeling (UTLM) method, which is a volume technique. The former allows accurate description of the scatterer's boundary and the field's radiation characteristics, but cannot model scattering by materials characterized by a non-uniform refraction index. The latter, on the contrary, can model a very broad range of materials, but is less accurate, since it has to rely on approximate absorbing boundary conditions. A method resulting in the hybridisation of BEM and UTLM can be used to construct a tool that takes into account both the interaction with non-uniform tissue and propagation in its environment. The project aims to describe in detail the implementation of the novel method, and deploy it in a heterogeneous distributed computing environment.
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Mazzolo, Lisa-Marie. "Étude et développement d’un outil efficace de simulation pour l’évaluation de SER : Application à la détection d’objets enfouis à partir de plates-formes aéroportées." Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0047.
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La détection d'objets enfouis, qu'il s'agisse d'engins explosifs dans un contexte militaire ou de structures archéologiques dans un contexte civil, constitue une préoccupation majeure. En termes de télédétection radar, les systèmes aéroportés, comme le radar à synthèse d’ouverture (SAR), permettent une imagerie non destructive des sous-sols tout en offrant la possibilité d'explorer de vastes zones avec une distance de sécurité par rapport à celles-ci. Cependant, leur efficacité pour la détection d’objets enfouis dépend de nombreux facteurs, tels que les caractéristiques diélectriques du sol, qui affectent la profondeur de pénétration des ondes électromagnétiques, la nature des cibles, le type d'émetteur... Une étude préliminaire, permettant de prédire la réponse des cibles en fonction des caractéristiques des systèmes et de la scène, serait alors un outil précieux pour évaluer les capacités de détection avant d'engager des campagnes de mesures.Cette thèse s'inscrit dans ce contexte, en se concentrant sur la recherche, le développement et l'optimisation d'un outil de simulation numérique destiné à évaluer précisément la surface équivalente radar (SER) d'objets enfouis. L'approche proposée repose sur une stratégie d'hybridation de solveurs FVTD (Finite Volume Time Domain) appliquée à des maillages hybrides cartésiens / non-structurés dans l'optique d'optimiser les coûts de calcul. En particulier, ces maillages hybrides permettent une représentation conforme des géométries courbes et une discrétisation spatiale localement adaptée aux vitesses de propagation des ondes électromagnétiques dans les différents milieux de la scène de calcul. La procédure d'obtention de ces maillages, basée sur le découpage du domaine de calcul en sous-domaines est détaillée, et les solveurs FVTD utilisés sont décrits en soulignant les choix effectués pour optimiser leur efficacité. L'implémentation des modèles permettant une description représentative du sol, la prise en compte précise d'une source de type onde plane et le calcul de champs lointains en présence d'un milieu avec pertes, est également abordée. L'hybridation des solveurs FVTD via une stratégie multi-domaines / multi-méthodes est présentée en détail, en mettant l'accent sur l'architecture logicielle proposée et en précisant la stabilité de la solution hybride ainsi que les enjeux de l'hybridation. Enfin, une comparaison de résultats simulés avec des données expérimentales obtenues dans le cadre d'une campagne de mesures mise en œuvre pour cette thèse, fournit une première appréciation des performances de l'outil de simulation développé. Pour conclure, la thèse met en avant la possibilité d'utiliser cet outil pour étudier l'impact des paramètres de configuration des systèmes radar sur la SER d'objets enfouis pour des scénarios donnésThe detection of buried objects, whether explosive devices in a military context or archaeological structures in a civilian context, is a major concern. In radar remote sensing, airborne systems such as Synthetic Aperture Radar (SAR) allow non-destructive imaging of subsurface environments while offering the possibility of exploring large areas from a safe distance. However, their effectiveness in detecting buried objects depends on many factors, such as the dielectric properties of the soil, which affect the penetration depth of electromagnetic waves, the nature of targets, and the type of transmitter... A preliminary study that predicts target response based on system and scene characteristics would be a valuable tool for assessing detection capabilities before launching measurement campaigns.This thesis addresses such context by focusing on the research, development, and optimization of a numerical simulation tool designed to accurately evaluate the radar cross-section (RCS) of buried objects. The proposed approach is based on a hybridization strategy using Finite Volume Time Domain (FVTD) solvers applied to hybrid Cartesian/unstructured meshes to optimize computational costs. More specifically, these hybrid meshes allow for a conformal representation of curved geometries and spatial discretization adapted to the varying electromagnetic wave propagation speeds in different media. The procedure for generating these meshes, based on the subdivision of the computational domain into subdomains is detailed, and used FVTD solvers are described, highlighting the choices made to optimize their efficiency. The implementation of models for representative soil description, accurate handling of plane-wave sources, and far-field calculations in lossy media are also addressed. The hybridization of FVTD solvers through a multi-domain/multi-method strategy is presented in detail, emphasizing proposed software architecture, the stability of the hybrid solution, and the challenges of hybridization. Finally, a comparison of simulated results with experimental data obtained during a measurement campaign conducted for this thesis provides an initial assessment of the performance of developed simulation tool. In conclusion, this thesis highlights the potential of this tool in studying the impact of radar system configuration parameters on buried objects RCS in given scenarios
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Sorensen, K. A. "A multigrid accelerated procedure for the solution of compressible fluid flows on unstructured hybrid meshes." Thesis, Swansea University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639089.
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A method for solving compressible fluid flow problems is described. The convergence of the solver is accelerated with the use of a multigrid scheme where the coarse meshes are created in an automatic way, using grid agglomeration. For viscous flows, a methodology for the application of unstructured hybrid meshes is proposed. A geometrically conservative, second order scheme for flows involving geometry movement for these meshes is presented. The performance of the method is illustrated in several examples of inviscid and viscous, steady-state and time-dependent flow. The complexity of the geometries considered spans from two-dimensional aerofoils to complex aircraft configurations.
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Larat, Adam. "Conception et Analyse de Schémas Distribuant le Résidu d'Ordre Très Élevé. Application à la Mécanique des Fluides." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2009. http://tel.archives-ouvertes.fr/tel-00502429.
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La simulation numérique est aujourd'hui un outils majeur dans la conception des objets aérodynamiques, que ce soit dans l'aéronautique, l'automobile, l'industrie navale, etc... Un des défis majeurs pour repousser les limites des codes de simulation est d'améliorer leur précision, tout en utilisant une quantité fixe de ressources (puissance et/ou temps de calcul). Cet objectif peut être atteint par deux approches différentes, soit en construisant une discrétisation fournissant sur un maillage donné une solution d'ordre très élevé, soit en construisant un schéma compact et massivement parallélisable, de manière à minimiser le temps de calcul en distribuant le problème sur un grand nombre de processeurs. Dans cette thèse, nous tentons de rassembler ces deux approches par le développement et l'implémentation de Schéma Distribuant le Résidu (RDS) d'ordre très élevé et de compacité maximale. Ce manuscrit commence par un rappel des principaux résultats mathématiques concernant les Lois de Conservation hyperboliques (CLs). Le but de cette première partie est de mettre en évidence les propriétés des solutions analytiques que nous cherchons à approcher, de manière à injecter ces propriétés dans celles de la solution discrète recherchée. Nous décrivons ensuite les trois étapes principales de la construction d'un schéma RD d'ordre très élevé : \begin{itemize} \item la représentation polynomiale d'ordre très élevé de la solution sur des polygones et des polyèdres; \item la description de méthodes distribuant le résidu de faible ordre, compactes et conservatives, consistantes avec une représentation polynomiale des données de très haut degré. Parmi elles, une attention particulière est donnée à la plus simple, issue d'une généralisation du schéma de Lax-Friedrichs (LxF); \item la mise en place d'une procédure préservant la positivité qui transforme tout schéma stable et linéaire, en un schéma non linéaire d'ordre très élevé, capturant les chocs de manière non oscillante. \end{itemize} Dans le manuscrit, nous montrons que les schémas obtenus par cette procédure sont consistants avec la CL considérée, qu'ils sont stables en norme $\L^{\infty}$ et qu'ils ont la bonne erreur de troncature. Même si tous ces développements théoriques ne sont démontrés que dans le cas de CL scalaires, des remarques au sujet des problèmes vectoriels sont faites dès que cela est possible. Malheureusement, lorsqu'on considère le schéma LxF, le problème algébrique non linéaire associé à la recherche de la solution stationnaire est en général mal posé. En particulier, on observe l'apparition de modes parasites de haute fréquence dans les régions de faible gradient. Ceux-ci sont éliminés grâce à un terme supplémentaire de stabilisation dont les effets et l'évaluation numérique sont précisément détaillés. Enfin, nous nous intéressons à une discrétisation correcte des conditions limites pour le schéma d'ordre élevé proposé. Cette théorie est ensuite illustrée sur des cas test scalaires bidimensionnels simples. Afin de montrer la généralité de notre approche, des maillages composés uniquement de triangles et des maillages hybrides, composés de triangles et de quadrangles, sont utilisés. Les résultats obtenus par ces tests confirment ce qui est attendu par la théorie et mettent en avant certains avantages des maillages hybrides. Nous considérons ensuite des solutions bidimensionnelles des équations d'Euler de la dynamique des gaz. Les résultats sont assez bons, mais on perd les pentes de convergence attendues dès que des conditions limite de paroi sont utilisées. Ce problème nécessite encore d'être étudié. Nous présentons alors l'implémentation parallèle du schéma. Celle-ci est analysée et illustrée à travers des cas test tridimensionnel de grande taille. Du fait de la relative nouveauté et de la complexité des problèmes tridimensionels, seuls des remarques qualitatives sont faites pour ces cas test : le comportement global semble être bon, mais plus de travail est encore nécessaire pour définir les propriétés du schémas en trois dimensions. Enfin, nous présentons une extension possible du schéma aux équations de Navier-Stokes dans laquelle les termes visqueux sont traités par une formulation de type Galerkin. La consistance de cette formulation avec les équations de Navier-Stokes est démontrée et quelques remarques au sujet de la précision du schéma sont soulevées. La méthode est validé sur une couche limite de Blasius pour laquelle nous obtenons des résultats satisfaisants. Ce travail offre une meilleure compréhension des propriétés générales des schémas RD d'ordre très élevé et soulève de nouvelles questions pour des améliorations futures. Ces améliorations devrait faire des schémas RD une alternative attractive aux discrétisations classiques FV ou ENO/WENO, aussi bien qu'aux schémas Galerkin Discontinu d'ordre très élevé, de plus en plus populaires.
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Munikrishna, N. "On Viscous Flux Discretization Procedures For Finite Volume And Meshless Solvers." Thesis, 2007. https://etd.iisc.ac.in/handle/2005/471.
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This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks.
Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations.
Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.
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Munikrishna, N. "On Viscous Flux Discretization Procedures For Finite Volume And Meshless Solvers." Thesis, 2007. http://hdl.handle.net/2005/471.
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This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks.
Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations.
Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.
Book chapters on the topic "Hybrid Cartesian/unstructured meshes"
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Abgrall, Rémi, Thomas Sonar, Oliver Friedrich, and Germain Billet. "High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes." In High-Order Methods for Computational Physics, 1–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03882-6_1.
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Duben, Alexey, and Tatiana Kozubskaya. "On Scale-Resolving Simulation of Turbulent Flows Using Higher-Accuracy Quasi-1D Schemes on Unstructured Meshes." In Progress in Hybrid RANS-LES Modelling, 169–78. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70031-1_14.
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Ginting, Bobby Minola, Punit Kumar Bhola, Christoph Ertl, Ralf-Peter Mundani, Markus Disse, and Ernst Rank. "Hybrid-Parallel Simulations and Visualisations of Real Flood and Tsunami Events Using Unstructured Meshes on High-Performance Cluster Systems." In Advances in Hydroinformatics, 867–88. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5436-0_67.
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Batten, P., C. Lambert, E. F. Toro, R. Saunders, and D. M. Causon. "A Temporal Refinement Algorithm for Unstructured Mesh Methods." In Numerical Methods for Fluid Dynamics V, 303–9. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198514800.003.0023.
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Abstract In recent years a number of promising new adaptive spatial refinement techniques have been developed for the numerical solution of partial differential equations on both structured and unstructured meshes[2, 1, 6, 4]. The use of dynamic local mesh adaption within a Cartesian mesh framework has proved extremely powerful in simulating a number of unsteady flows involving moving shock waves[2, 5, 3]. Aside from the obvious benefit of providing greater resolution for a fixed computational cost, the success of these adaptive Cartesian mesh methods can be attributed to the use of matured, high resolution total variation diminishing type schemes and the application of temporal refinement, a technique which allows different regions of the physical domain to advance with different time steps. Whilst bounded higher order methods for unstructured elements are continuing to improve, temporal refinement appears to be continuing an exclusive deployment in adaptive Cartesian mesh methods.
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Quirk, James J. "A cartesian grid scheme for gas dynamic flows that involve complex geometries." In Numerical Methods for Fluid Dynamics, 385–92. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198536963.003.0031.
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Abstract The desire to simulate flows around geometrically complex bodies has led many members of the shock capturing community to abandon schemes which employ body-fitted grids in favour of schemes which employ unstructured meshes. Now such is the success of unstructured grids, there is a danger that they will become de rigueur. Given the ever increasing reliance placed on computational results, such a state of affairs would give cause for some concern. If nothing else, the exercise of using several computer codes to cross check numerical results becomes ill-founded if all codes follow the same methodology. In this paper we outline an alternative approach for dealing with complex two-dimensional geometries, the so-called cartesian boundary method; solid bodies blank out areas of a background cartesian mesh and the cut cells which arise along solid boundaries are singled out for special treatment during the integration of the discretized flow solution.
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Peiró, J., and A. I. Sayma. "A 3-D Unstructured Multigrid Navier-Stokes Solver." In Numerical Methods for Fluid Dynamics V, 533–39. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198514800.003.0051.
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Abstract Unstructured mesh methods have proven to be a useful practical tool for aeronautical design. Currently, the process of mesh generation and computation of inviscid flows past complex configurations such as a full aircraft can be completed in a matter of days. The meshes used for inviscid computations consist, in general, of tetrahedral elements of aspect ratio close to unity [1]. The use of such meshes for the simulation of high Reynolds number flows is computationally unfeasible due to the very small mesh sizes required in the near-wall regions where viscous layers are present. A compromise between economy and accuracy can be achieved by the use of elements that are stretched along the flow direction in those regions. Current mesh generation methods can be used to produce these stretched elements ([2],[4]) but the quality of the generated elements is very difficult to control. An alternative method is the use of an hybrid approach in which the mesh near the solid surfaces is generated by an hyperbolic type mesh generator whilst the region outside the viscous layer is discretized using the conventional approach [5].
Conference papers on the topic "Hybrid Cartesian/unstructured meshes"
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Jung, Yong, Bharath Govindarajan, and James Baeder. "A Hamiltonian-Strand Approach for Aerodynamic Flows Using Overset and Hybrid Meshes." In Vertical Flight Society 72nd Annual Forum & Technology Display, 1–20. The Vertical Flight Society, 2016. http://dx.doi.org/10.4050/f-0072-2016-11387.
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A solution framework using Hamiltonian paths and strand grids (HAMSTR) is presented for three-dimensional flows on overset and hybrid meshes. The methodology creates a volume mesh starting from an unstructured surface mesh that can be comprised of mixed triangular-quadrilateral elements. "Linelets" through the meshes are found in a robust manner and the solver uses line-implicit schemes and high-order reconstruction schemes along these linelets, similar to a structured solver. The mesh system is also extended to utilize overset meshes. This overset technique allows for multiple mesh systems, which consists of a near-body Hamiltonian/Strand grid and off-body Cartesian nested meshes. The generalized approach to obtaining the Hamiltonian paths allows for initially structured and unstructured meshes to be quilted together to form a unified grid. In such cases, Hamiltonian paths can cross themselves; however, no changes are necessary for the flow solver. Finally, the integration framework between the various components of the code suite is performed using Python to allow for ease of integration in the future to other codes. Aerodynamic flows past an airfoil, sphere, wing and non-lifting rotor are presented using the Hamiltonian/Strand approach and good agreement was observed against experimental results as well as solutions obtained from traditional structured solvers.
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Jung, Min Kyu, and Oh Joon Kwon. "Development of a 2-D Flow Solver on Hybrid Unstructured and Adaptive Cartesian Meshes." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-01008.
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In the present study, a two-dimensional hybrid flow solver has been developed for the accurate and efficient simulation of steady and unsteady flow fields. The flow solver was cast to accommodate two different topologies of computational meshes. Triangular meshes are adopted in the near-body region such that complex geometric configurations can be easily modeled, while adaptive Cartesian meshes are utilized in the off-body region to resolve the flow more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. Adaptive Cartesian meshes can be generated automatically and allow to handle data efficiently via quad-tree data structures. A chimera mesh approach has been employed to link the two flow regimes adopting each mesh topology. A second-order accurate vertex-centered scheme and a 3rd- or 5th-order accurate cell-centered WENO scheme have been utilized in the near-body region and in the off-body region, respectively. Validations were made for the unsteady inviscid vortex convection and the steady and unsteady turbulent flows over an NACA0012 airfoil, and the results were compared with other computational and experimental results.
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Dawes, William N. "Twenty Five Years of Mesh Generation: A Personal Perspective." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-05016.
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Since starting research in CFD the early 1980’s as a PhD Student I have worked with a variety of mesh types and topologies. The main application areas have been in aerospace, mostly in turbomachinery, but also in racing car aerodynamics and in the oil & gas process industries. The first meshes I used were simple, sheared H meshes for blade-to-blade flows; these were — and still are — perfectly adequate for this class of simulation and are in use to this day in routine design all around the world. However, most application areas are fundamentally more complex, both in terms of geometry and of flow physics, and necessitate more complex mesh systems. Current simulation trends are relentlessly towards using fully featured, fully 3D geometry and effective, high-productivity mesh generation systems have become of central significance. Over the past twenty five years I have worked with simple structured meshes, multi-block meshes, unstructured meshes based both on Delaunay and advancing front paradigms and, more recently, on octree-based cut-Cartesian meshes and associated body-conformal, hybrid meshes. This has gone hand in hand with increasing interest in computational geometry and geometry editing and parameterisation to support automated design optimisation. This paper represents my personal perspective on these experiences.
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Stalnaker, John, and Michael Robinson. "Computation of Stability Derivatives of Spinning Missiles Using Unstructured Cartesian Meshes." In 20th AIAA Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-2802.
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Kozubskaya, Tatiana, and Pavel Bakhvalov. "On Efficient Vertex-Centered Schemes on Hybrid Unstructured Meshes." In 22nd AIAA/CEAS Aeroacoustics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-2966.
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Lepage, C., F. Suerich-Gulick, and W. Habashi. "Anisotropic 3-D mesh adaptation on unstructured hybrid meshes." In 40th AIAA Aerospace Sciences Meeting & Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2002. http://dx.doi.org/10.2514/6.2002-859.
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Hosangadi, A., P. Cavallo, S. Arunajatesan, R. Ungewitter, and R. Lee. "Aero-propulsive jet interaction simulations using hybrid unstructured meshes." In 35th Joint Propulsion Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-2119.
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Ito, Yasushi, Alan Shih, Bharat Soni, and Kazuhiro Nakahashi. "An Approach to Generate High Quality Unstructured Hybrid Meshes." In 44th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2006. http://dx.doi.org/10.2514/6.2006-530.
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Karman, Steve, and Perry Wooden. "CFD Modeling of F-35 Using Hybrid Unstructured Meshes." In 19th AIAA Computational Fluid Dynamics. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-3662.
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Ravindran, Sreekanth, and Stephen Woodruff. "Model-Invariant Hybrid RANS-LES Computations on Unstructured Meshes." In 2018 Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-3408.
Full textReports on the topic "Hybrid Cartesian/unstructured meshes"
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Karniadakis, George E. High-Order Algorithms for 3D Plasma Simulations on Unstructured and Hybrid Meshes. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada381671.
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Wang, Z. J., T. Haga, and H. Gao. A Unifying High-Order Method for the Navier-Stokes Equations on Hybrid Unstructured Meshes. Fort Belvoir, VA: Defense Technical Information Center, April 2013. http://dx.doi.org/10.21236/ada583716.
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Menon, Suresh, Tim Gallagher, and Balaji Muralidharan. Hybrid Solution-Adaptive Unstructured Cartesian Method for Large-Eddy Simulation of Detonation in Multi-Phase Turbulent Reactive Mixtures. Fort Belvoir, VA: Defense Technical Information Center, March 2012. http://dx.doi.org/10.21236/ada567123.
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