Relevant bibliographies by topics / Staggered grids finite difference

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  2. Dissertations / Theses
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Academic literature on the topic 'Staggered grids finite difference'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Staggered grids finite difference"

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Bernth, Henrik, and Chris Chapman. "A comparison of the dispersion relations for anisotropic elastodynamic finite-difference grids." GEOPHYSICS 76, no. 3 (2011): WA43—WA50. http://dx.doi.org/10.1190/1.3555530.

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Several staggered grid schemes have been suggested for performing finite-difference calculations for the elastic wave equations. In this paper, the dispersion relationships and related computational requirements for the Lebedev and rotated staggered grids for anisotropic, elastic, finite-difference calculations in smooth models are analyzed and compared. These grids are related to a popular staggered grid for the isotropic problem, the Virieux grid. The Lebedev grid decomposes into Virieux grids, two in two dimensions and four in three dimensions, which decouple in isotropic media. Therefore the Lebedev scheme will have twice or four times the computational requirements, memory, and CPU as the Virieux grid but can be used with general anisotropy. In two dimensions, the rotated staggered grid is exactly equivalent to the Lebedev grid, but in three dimensions it is fundamentally different. The numerical dispersion in finite-difference grids depends on the direction of propagation and the grid type and parameters. A joint numerical dispersion relation for the two grids types in the isotropic case is derived. In order to compare the computational requirements for the two grid types, the dispersion, averaged over propagation direction and medium velocity are calculated. Setting the parameters so the average dispersion is equal for the two grids, the computational requirements of the two grid types are compared. In three dimensions, the rotated staggered grid requires at least 20% more memory for the field data and at least twice as many number of floating point operations and memory accesses, so the Lebedev grid is more efficient and is to be preferred.
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Di Bartolo, Leandro, Leandro Lopes, and Luis Juracy Rangel Lemos. "High-order finite-difference approximations to solve pseudoacoustic equations in 3D VTI media." GEOPHYSICS 82, no. 5 (2017): T225—T235. http://dx.doi.org/10.1190/geo2016-0589.1.

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Pseudoacoustic algorithms are very fast in comparison with full elastic ones for vertical transversely isotropic (VTI) modeling, so they are suitable for many applications, especially reverse time migration. Finite differences using simple grids are commonly used to solve pseudoacoustic equations. We have developed and implemented general high-order 3D pseudoacoustic transversely isotropic formulations. The focus is the development of staggered-grid finite-difference algorithms, known for their superior numerical properties. The staggered-grid schemes based on first-order velocity-stress wave equations are developed in detail as well as schemes based on direct application to second-order stress equations. This last case uses the recently presented equivalent staggered-grid theory, resulting in a staggered-grid scheme that overcomes the problem of large memory requirement. Two examples are presented: a 3D simulation and a prestack reverse time migration application, and we perform a numerical analysis regarding computational cost and precision. The errors of the new schemes are smaller than the existing nonstaggered-grid schemes. In comparison with existing staggered-grid schemes, they require 25% less memory and only have slightly greater computational cost.
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Igel, Heiner, Peter Mora, and Bruno Riollet. "Anisotropic wave propagation through finite‐difference grids." GEOPHYSICS 60, no. 4 (1995): 1203–16. http://dx.doi.org/10.1190/1.1443849.

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An algorithm is presented to solve the elastic‐wave equation by replacing the partial differentials with finite differences. It enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models. The space derivatives are calculated using discrete convolution sums, while the time derivatives are replaced by a truncated Taylor expansion. A centered finite difference scheme in Cartesian coordinates is used for the space derivatives leading to staggered grids. The use of finite difference approximations to the partial derivatives results in a frequency‐dependent error in the group and phase velocities of waves. For anisotropic media, the use of staggered grids implies that some of the elements of the stress and strain tensors must be interpolated to calculate the Hook sum. This interpolation induces an additional error in the wave properties. The overall error depends on the precision of the derivative and interpolation operators, the anisotropic symmetry system, its orientation and the degree of anisotropy. The dispersion relation for the homogeneous case was derived for the proposed scheme. Since we use a general description of convolution sums to describe the finite difference operators, the numerical wave properties can be calculated for any space operator and an arbitrary homogeneous elastic model. In particular, phase and group velocities of the three wave types can be determined in any direction. We demonstrate that waves can be modeled accurately even through models with strong anisotropy when the operators are properly designed.
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Huang, Huaxiong, and Ming Li. "Finite-difference approximation for the velocity-vorticity formulation on staggered and non-staggered grids." Computers & Fluids 26, no. 1 (1997): 59–82. http://dx.doi.org/10.1016/s0045-7930(96)00028-x.

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Armfield, S. W. "Finite difference solutions of the Navier-Stokes equations on staggered and non-staggered grids." Computers & Fluids 20, no. 1 (1991): 1–17. http://dx.doi.org/10.1016/0045-7930(91)90023-b.

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Zhang, Jie, Fan Shun Meng, and Yang Sen Li. "The Study of the Difference Methods with Variable Grids Seismic Wave Numerical Simulation in Multi-Scale Complex Media." Advanced Materials Research 1055 (November 2014): 254–58. http://dx.doi.org/10.4028/www.scientific.net/amr.1055.254.

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In the process of seismic wave field numerical simulation using finite difference method, the simulation accuracy and computational efficiency is one of the keys to the problem which is especially important to the numerical simulation of small scale geological body which velocity changes violently. In order to describe the local structure of medium subtly and guarantee the efficiency of the simulation, this article introduces the variable grid finite difference method to the staggered grid high-order finite difference numerical simulation on the basic of the traditional staggered grid finite difference algorithm to improve the staggered grid spatial algorithm and avoid the reduction of the simulation accuracy and computational efficiency caused by the interpolation factor. The results show that the variable staggered grid numerical simulation of finite difference algorithm can accurately depict the space variation of underground medium physical properties to further enhance the adaptability of numerical simulation of complex medium, it also can provide reliable basis for wave field imaging and the combined interpretation of p-wave and s-wave.
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Pitarka, Arben. "3D Elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing." Bulletin of the Seismological Society of America 89, no. 1 (1999): 54–68. http://dx.doi.org/10.1785/bssa0890010054.

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Abstract This article provides a technique to model seismic motions in 3D elastic media using fourth-order staggered-grid finite-difference (FD) operators implemented on a mesh with nonuniform grid spacing. The accuracy of the proposed technique has been tested through comparisons with analytical solutions, conventional 3D staggered-grid FD with uniform grid spacing, and reflectivity methods for a variety of velocity models. Numerical tests with nonuniform grids suggest that the method allows sufficiently accurate modeling when the grid sampling rate is at least 6 grid points per shortest shear wavelength. The applicability for a finite fault with non-uniform distribution of point sources is also confirmed. The use of nonuniform spacing improves the efficiency of the FD methods when applied to large-scale structures by partially avoiding the spatial oversampling introduced by the uniform spacing in zones with high velocity. The significant reduction in computer memory that can be obtained by the new technique improves the efficiency of the 3D-FD method at handling shorter wavelengths, larger areas, or more realistic 3D velocity structures.
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KÄSER, MARTIN, HEINER IGEL, MALCOLM SAMBRIDGE, and JEAN BRAUN. "A COMPARATIVE STUDY OF EXPLICIT DIFFERENTIAL OPERATORS ON ARBITRARY GRIDS." Journal of Computational Acoustics 09, no. 03 (2001): 1111–25. http://dx.doi.org/10.1142/s0218396x01000838.

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We compare explicit differential operators for unstructured grids and their accuracy with the aim of solving time-dependent partial differential equations in geophysical applications. As many problems suggest the use of staggered grids we investigate different schemes for the calculation of space derivatives on two separate grids. The differential operators are explicit and local in the sense that they use only information of the function in their nearest neighborhood, so that no matrix inversion is necessary. This makes this approach well-suited for parallelization. Differential weights are obtained either with the finite-volume method or using natural neighbor coordinates. Unstructured grids have advantages concerning the simulation of complex geometries and boundaries. Our results show that while in general triangular (hexagonal) grids perform worse than standard finite-difference approaches, the effects of grid irregularities on the accuracy of the space derivatives are comparably small for realistic grids. This suggests that such a finite-difference-like approach to unstructured grids may be an alternative to other irregular grid methods such as the finite-element technique.
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Bohlen, Thomas, and Erik H. Saenger. "Accuracy of heterogeneous staggered-grid finite-difference modeling of Rayleigh waves." GEOPHYSICS 71, no. 4 (2006): T109—T115. http://dx.doi.org/10.1190/1.2213051.

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Heterogeneous finite-difference (FD) modeling assumes that the boundary conditions of the elastic wavefield between material discontinuities are implicitly fulfilled by the distribution of the elastic parameters on the numerical grid. It is widely applied to weak elastic contrasts between geologic formations inside the earth. We test the accuracy at the free surface of the earth. The accuracy for modeling Rayleigh waves using the conventional standard staggered-grid (SSG) and the rotated staggered grid (RSG) is investigated. The accuracy tests reveal that one cannot rely on conventional numerical dispersion discretization criteria. A higher sampling is necessary to obtain acceptable accuracy. In the case of planar free surfaces aligned with the grid, 15 to 30 grid points per minimum wavelength of the Rayleigh wave are required. The widely used explicit boundary condition, the so-called image method, produces similar accuracy and requires approximately half the sampling of the wavefield compared to heterogeneous free-surface modeling. For a free-surface not aligned with the grid (surface topography), the error increases significantly and varies with the dip angle of the interface. For an irregular interface, the RSG scheme is more accurate than the SSG scheme. The RSG scheme, however, requires 60 grid points per minimum wavelength to achieve good accuracy for all dip angles. The high computation requirements for 3D simulations on such fine grids limit the application of heterogenous modeling in the presence of complex surface topography.
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Pérez Solano, C. A., D. Donno, and H. Chauris. "Finite-difference strategy for elastic wave modelling on curved staggered grids." Computational Geosciences 20, no. 1 (2016): 245–64. http://dx.doi.org/10.1007/s10596-016-9561-8.

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Dissertations / Theses on the topic "Staggered grids finite difference"

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Trenchant, Vincent. "Discrétisation et commande frontière de systèmes vibro-acoustiques, une approche hamiltonienne à ports." Thesis, Bourgogne Franche-Comté, 2017. http://www.theses.fr/2017UBFCD066/document.

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Cette thèse répond à une problématique de commande frontière d’une conduite acoustique dont l’actionnement est assuré par un réseau d’actionneurs/capteurs co-localisés constituant une peau active. Pour faire face au caractère intrinsèquement multiphysique de ce problème vibro-acoustique, nous avons choisi dans cette thèse d’employer une approche hamiltonienne à ports, approche structurée basée sur la représentation des échanges entre différents domaines énergétiques au sein d’un système et entre différents systèmes. Nous avons proposé une modélisation hamiltonienne à ports de l’équation d’onde interconnectée à la frontière au système d’actionnement distribué, correspondant à une formulation 2D du problème physique. Nous avons développé une méthode de discrétisation spatiale basée sur l’utilisation de différences finies sur plusieurs grilles en quinconce qui préserve la structure hamiltonienne à ports de l’équation d’onde. Cette méthode permet en outre d’interconnecter facilement le système discrétisé avec d’autres sous-systèmes, dans le but de mettre en place un actionnement par exemple. Son principal avantage sur d’autres méthodes préservatives de structure réside dans sa simplicité de mise en œuvre qui découle de l’utilisation de différences finies. Concernant la commande du système vibro-acoustique, nous avons proposé une méthode de synthèse de loi de commande distribuée pour les systèmes régis par deux lois de conservation en 1D. L’originalité de cette méthode réside en le fait qu’elle repose sur le calcul d’invariants structuraux (fonctions de Casimir) exploités afin de modifier la structure du système en boucle fermée. Les conditions d’application sur un système 2D sont étudiées et des résultats numériques valident les lois de commande synthétisées<br>This thesis deals with the boundary control of an acoustic by a network of co-localised sensors/actuators which constitutes a smart skin. In order to cope with this multiphysical problem, we chose to place our study in the framework of port-Hamiltonian systems, a structured approach based on the representation of energy exchanges between different energy domains between different systems of subsystems. We proposed a port-Hamiltonian model of the wave equation interconnected through its boundary to the distributed actuation system, which corresponds to a 2D formulation of the physical problem. We developed a spatial discretization method based on the use of finite differences on several staggered grids that preserve the port-Hamiltonian structure of the wave equation. This method also permits to easily interconnect the discretized system with other subsystems, which is convenient for instance for control purposes. Its main advantage over other structure preserving methods is its simplicity of implementation which stems from the use of finite differences. In order to control the vibro-acoustic system, we proposed a control law synthesis method for systems governed by two conservation laws in 1D. The originality of this method lies in the fact that it relies on the computation of structural invariants (Casimir functions) exploited in order to modify the structure of the system in closed loop. The conditions of application of these laws on a 2D system are studied and numerical results validate the synthesized control laws
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Bø, Ruben Kristoffer Thomasse. "On Mimetic Finite Difference Methods for Grids with Curved Faces." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19356.

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In this thesis the mimetic finite difference method for grids with curved faces is presented, implemented and tested with an emphasis on applications in reservoir simulation. The thesis gives a brief introduction to reservoir modeling and introduce the mimetic method for flat and for curved faces. Then the continuity condition for the curved mimetic method is discussed. It is shown that the suggested continuity condition is not valid for cases with a difference in permeability between two cells separated by a curved face. An alternative continuity condition is discussed and implemented. Numerical examples confirm that the original continuity condition is incorrect for general examples with heterogeneous permeability. Numerical examples for the alternative continuity condition shows that it is correct for simple cases, and that it gives no gain in accuracy compared to the mimetic method. In conclusion the curved mimetic method is primarily of academic interest.
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Stålberg, Erik. "A high order method for simulation of fluid flow in complex geometries." Licentiate thesis, KTH, Mechanics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-322.

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<p>A numerical high order difference method is developed for solution of the incompressible Navier-Stokes equations. The solution is determined on a staggered curvilinear grid in two dimensions and by a Fourier expansion in the third dimension. The description in curvilinear body-fitted coordinates is obtained by an orthogonal mapping of the equations to a rectangular grid where space derivatives are determined by compact fourth order approximations. The time derivative is discretized with a second order backward difference method in a semi-implicit scheme, where the nonlinear terms are linearly extrapolated with second order accuracy.</p><p>An approximate block factorization technique is used in an iterative scheme to solve the large linear system resulting from the discretization in each time step. The solver algorithm consists of a combination of outer and inner iterations. An outer iteration step involves the solution of two sub-systems, one for prediction of the velocities and one for solution of the pressure. No boundary conditions for the intermediate variables in the splitting are needed and second order time accurate pressure solutions can be obtained.</p><p>The method has experimentally been validated in earlier studies. Here it is validated for flow past a circular cylinder as an example of a physical test case and the fourth order method is shown to be efficient in terms of grid resolution. The method is applied to external flow past a parabolic body and internal flow in an asymmetric diffuser in order to investigate the performance in two different curvilinear geometries and to give directions for future development of the method. It is concluded that the novel formulation of boundary conditions need further investigation.</p><p>A new iterative solution method for prediction of velocities allows for larger time steps due to less restrictive convergence constraints.</p>
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Peixoto, Pedro da Silva. "Análise de discretizações e interpolações em malhas icosaédricas e aplicações em modelos de transporte semi-lagrangianos." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-26062013-174032/.

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A esfera é utilizada como domínio computacional na modelagem de diversos fenômenos físicos, como em previsão numérica do tempo. Sua discretização pode ser feita de diversas formas, sendo comum o uso de malha regulares em latitude/longitude. Recentemente, também para melhor uso de computação paralela, há uma tendência ao uso de malhas mais isotrópicas, dentre as quais a icosaédrica. Apesar de já existirem modelos atmosféricos que usam malhas icosaédricas, não há consenso sobre as metodologias mais adequadas a esse tipo de malha. Nos propusemos, portanto, a estudar em detalhe diversos fatores envolvidos no desenvolvimento de modelos atmosféricos globais usando malhas geodésicas icosaédricas. A discretização usual por volumes finitos para divergente de um campo vetorial utiliza como base o Teorema da Divergência e a regra do ponto médio nas arestas das células computacionais. A distribuição do erro obtida com esse método apresenta uma forte relação com características geométricas da malha. Definimos o conceito geométrico de alinhamento de células computacionais e desenvolvemos uma teoria que serve de base para explicar interferências de malha na discretização usual do divergente. Destacamos os impactos de certas relações de alinhamento das células na ordem da discretização do método. A teoria desenvolvida se aplica a qualquer malha geodésica e também pode ser usada para os operadores rotacional e laplaciano. Investigamos diversos métodos de interpolação na esfera adequados a malhas icosaédricas, e abordamos o problema de interpolação e reconstrução vetorial na esfera em malhas deslocadas. Usamos métodos alternativos de reconstrução vetorial aos usados na literatura, em particular, desenvolvemos um método híbrido de baixo custo e boa precisão. Por fim, utilizamos as técnicas de discretização, interpolação e reconstrução vetorial analisadas em um método semi-lagrangiano para o transporte na esfera em malhas geodésicas icosaédricas. Realizamos experimentos computacionais de transporte, incluindo testes de deformações na distribuição do campo transportado, que mostraram a adequação da metodologia para uso em modelos atmosféricos globais. A plataforma computacional desenvolvida nesta tese, incluindo geração de malhas, interpolações, reconstruções vetoriais e um modelo de transporte, fornece uma base para o futuro desenvolvimento de um modelo atmosférico global em malhas icosaédricas.<br>Spherical domains are used to model many physical phenomena, as, for instance, global numerical weather prediction. The sphere can be discretized in several ways, as for example a regular latitude-longitude grid. Recently, also motivated by a better use of parallel computers, more isotropic grids have been adopted in atmospheric global circulation models. Among those, the icosahedral grids are promising. Which kind of discretization methods and interpolation schemes are the best to use on those grids are still a research subject. Discretization of the sphere may be done in many ways and, recently, to make better use of computational resources, researchers are adopting more isotropic grids, such as the icosahedral one. In this thesis, we investigate in detail the numerical methodology to be used in atmospheric models on icosahedral grids. The usual finite volume method of discretization of the divergence of a vector field is based on the divergence theorem and makes use of the midpoint rule for integration on the edges of computational cells. The error distribution obtained with this method usually presents a strong correlation with some characteristics of the icosahedral grid. We introduced the concept of cell alignment and developed a theory which explains the grid imprinting patterns observed with the usual divergence discretization. We show how grid alignment impacts in the order of the divergence discretization. The theory developed applies to any geodesic grid and can also be used for other operators such as curl and Laplacian. Several interpolation schemes suitable for icosahedral grids were analysed, including the vector interpolation and reconstruction problem on staggered grids. We considered alternative vector reconstruction methods, in particular, we developed a hybrid low cost and good precision method. Finally, employing the discretizations and interpolations previously analysed, we developed a semi-Lagrangian transport method for geodesic icosahedral grids. Several tests were carried out, including deformational test cases, which demonstrated that the methodology is suitable to use in global atmospheric models. The computational platform developed in this thesis, including mesh generation, interpolation, vector reconstruction and the transport model, provides a basis for future development of global atmospheric models on icosahedral grids.
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Albin, Eric. "Contribution à la modélisation numérique des flammes turbulentes : comparaison DNS-EEM-Expériences." Phd thesis, INSA de Rouen, 2010. http://tel.archives-ouvertes.fr/tel-00557908.

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La dynamique des flammes de prémélange est étudiée par deux approches numériques différentes. La première résout les équations compressibles de Navier-Stokes avec une chimie simplifiée (DNS). Afin de réduire les coûts de calcul, nous analysons et développons un schéma numérique à grille décalée. Le traitement des ondes acoustiques aux sorties est connu pour rendre les flammes cylindriques légèrement carrées. Ces déformations non-physiques sont expliquées en mettant en évidence la modélisation insuffisamment précise de l'accélération du fluide lorsque l'écoulement est oblique à la sortie. Une étude paramétrique et statistique de flammes turbulentes est menée en 2D et une simulation parallèle 3D est réalisée dans un domaine de (3cm)3. En considérant la flamme infiniment mince, l'approche EEM diminue considérablement les coûts de calcul. Les mêmes simulations sont réalisées et comparées aux résultats de DNS pour tester la capacité du modèle EEM à fournir des résultats quantitatifs.
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Gunawan, Harry Putu. "Numerical simulation of shallow water equations and related models." Thesis, Paris Est, 2015. http://www.theses.fr/2015PEST1010/document.

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Cette thèse porte sur l'approximation numérique des équations de Saint-Venant et de quelques problèmes qui leur sont reliés. Dans la première partie, nous analysons les propriétés mathématiques et les applications des schémas numériques sur grilles décalées. La robustesse de ces schémas est prouvée sur des applications telles que les équations de Saint-Venant dans un domaine en rotation, en vue des écoulements géostrophiques, ainsi que l'extension de ces équations au cas visqueux. Dans la seconde partie, nous présentons des modèles basés sur les équations de Saint-Venant. Nous commençons par étudier le couplage avec l'équation d'Exner, qui porte sur le transport des sédiments. Nous observons des propriétés de convergence numérique vers la solution exacte dans un cas de solution analytique, et nous constatons un bon accord avec des données expérimentales dans le cas de la rupture de barrage avec fond érodable. Nous continuons par l'étude d'un schéma numérique, basé sur une méthode de volumes finis colocalisés (HLLC) pour l'approximation du modèle de Richard-Gavrilyuk. Ce modèle étend les équations de Saint-Venant au cas des écoulements avec cisaillement. Des tests numériques montrent la validité du schéma<br>This thesis is devoted to the numerical approximation of the shallow water equations and of some related models. In the first part, we analyze the mathematical properties and the applications of the staggered grid scheme. The robustness of this scheme is validated on various applications such as the rotating shallow water equations for geostrophic flows model and viscous shallow water equations. In the second part, we consider some related models. Firstly focusing on the coupling between the Exner equation and the shallow water equations, modelling bedload sediment transport, we observe in a particular case the numerical convergence of the scheme to the exact solution, as well as a good agreement with the experimental data in the dam-break with erodible bottom test. Secondly, we present a numerical scheme based on the finite volume collocated scheme (HLLC) in order to approximate the Richard-Gavrilyuk model. This model is an extension of the shallow water model, fit for modelling the shear shallow water flows. Some numerical tests provide a validation of the scheme
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Bénézet, Cyril. "Study of numerical methods for partial hedging and switching problems with costs uncertainty." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7079.

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Nous apportons dans cette thèse quelques contributions à l’étude théorique et numérique de certains problèmes de contrôle stochastique, ainsi que leurs applications aux mathématiques financières et à la gestion des risques financiers. Ces applications portent sur des problématiques de valorisation et de couverture faibles de produits financiers, ainsi que sur des problématiques réglementaires. Nous proposons des méthodes numériques afin de calculer efficacement ces quantités pour lesquelles il n’existe pas de formule explicite. Enfin, nous étudions les équations différentielles stochastiques rétrogrades liées à de nouveaux problèmes de switching, avec incertitude sur les coûts<br>In this thesis, we give some contributions to the theoretical and numerical study to some stochastic optimal control problems, and their applications to financial mathematics and risk management. These applications are related to weak pricing and hedging of financial products and to regulation issues. We develop numerical methods in order to compute efficiently these quantities, when no closed formulae are available. We also study backward stochastic differential equations linked to some new switching problems, with costs uncertainty
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"Finite difference approximations for parabolic systems on grids with irregular nodes." Tulane University, 1998.

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We derive a priori and a posteriori estimates for the error of the bi-linear interpolation polynomial for finite difference approximations of the solutions of parabolic systems on grids with irregular nodes. The estimates are developed for the $L\sp2$ norm, the $H\sp1$ semi-norm, and the $H\sp1$ norm of the error. We use the a posteriori error estimates of the interpolation polynomial to determine the 'high error' regions which require a finer mesh for computation. We derive and implement consistent computational stencils for the spatial derivatives at the nodes on the interface of regions of different levels of refinement. We use local error estimation and global computation<br>acase@tulane.edu
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Tsai, Jin Lu, and 蔡季陸. "Finite Difference Method Comdined with Boundary-fitted Orthogonal Grids on 3-D Groundwater Flow." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/92984471416515720771.

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碩士<br>國立臺灣大學<br>土木工程學研究所<br>89<br>The purpose of this paper is to incorporate MODFLOW (McDonald and Harbaugh, 1988) finite difference method (FDM) with the technique of a numerical method to generate boundary-fitted orthogonal grids. It is intended to build a new numerical model MODFLOW/T to simulate a three dimensional groundwater problem with irregular boundaries in the horizontal plane. The new model MODFLOW/T is to convert the horizontal irregular- boundary domain onto a transformed rectangle with four straight boundaries to generate orthogonal grids. By applying FDM to this domain, this new model is employed to simulate a 3-D groundwater system. It is intended to overcome the limitations of FDM irregular domains. By skillfully reformulating the governing equation, the original structure of MODFLOW has not been changed; only minor modifications based on the curvilinear orthogonal grids are added so that applications of original MODFLOW remain unchanged on input format. This paper first describes the procedures of finite difference method used in MODFLOW, including formulation of the governing equations and finite difference approximation. A technique of region mapping using boundary integral element method is then followed. Finally, the technique to generate boundary-fitted orthogonal grids is incorporated into MODFLOW to solve 3-D groundwater problems in a region with horizontal irregular boundaries. Results of the modified MODFLOW are verified in two benchmark problems. The results of this analysis show integration of the MODFLOW with boundary-fitted orthogonal grids not only saves time to generate meshes but also diminishes the errors induced by irregular boundaries. Thus, the modified MODFLOW/T is more applicable to irregular regions in simulating groundwater flow problems.
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Chi, Chang Han, and 張漢錡. "Dynamic Analysis of the Flexible Quick-Return Mechanism by Fixed and Variable Finite-Difference Grids." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/54409730200580624186.

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碩士<br>中原大學<br>機械工程學系<br>87<br>The finite difference method (FDM) with fixed and variable grids is proposed to approximate the numerical solutions of a flexible quick-return mechanism, which involves a flexible rod with time-dependent length. In the dynamic analysis and simulation, the flexible rod is divided into two regions. Each region is modeled by the Timoshenko- and Euler-beam theories. It is found that (1) the fixed-grid method, where the moving boundary is often located between two neighboring grid points, breaks down when the boundary moves a distance larger than an increment space during a time step. (2) The possibility of break down can be avoided via the variable-grid method, in which a coordinate transformation is employed to fix the moving boundary. The numerical results are provided to compare with the previous works.
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Books on the topic "Staggered grids finite difference"

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Zingg, D. W. Finite-difference schemes on regular triangular grids. Academic Press, 1993.

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Stanly, Steinberg, ed. Conservative finite-difference methods on general grids. CRC Press, 1996.

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Steger, Joseph L. Implicit finite difference simulation of flow about arbitrary geometrics with application to airfoils. AIAA, 1987.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Zingg, D. W. A review of high-order and optimized finite-difference methods for simulating linear wave phenomena. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1996.

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Zingg, D. W. A review of high-order and optimized finite-difference methods for simulating linear wave phenomena. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1996.

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Book chapters on the topic "Staggered grids finite difference"

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Wesseling, Pieter. "Finite volume and finite difference discretization on nonuniform grids." In Principles of Computational Fluid Dynamics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05146-3_3.

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Dorodnitsyn, Vladimir. "Continuous symmetries of finite-difference evolution equations and grids." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1996. http://dx.doi.org/10.1090/crmp/009/10.

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Gibou, Frédéric, Chohong Min, and Hector Ceniceros. "Finite Difference Schemes for Incompressible Flows on Fully Adaptive Grids." In Free Boundary Problems. Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/978-3-7643-7719-9_20.

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Karamzin, Yury N., Tatiana A. Kudryashova, Sergey V. Polyakov, and Viktoriia O. Podryga. "Finite Difference Schemes on Locally Refined Cartesian Grids for the Solution of Gas Dynamic Problems on the Basis of Quasigasdynamics Equations." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_36.

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Sanders, Richard. "A Staggered Mesh Finite Difference Scheme for the Computation of Hypersonic Euler Flows." In Hypersonic Flows for Reentry Problems. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76527-8_47.

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Matus, Piotr P., Vladimir I. Mazhukin, and Igor E. Mozolevsky. "Stability of Finite Difference Schemes on Non-uniform Spatial-Time-Grids." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45262-1_67.

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Ndjinga, Michaël, and Katia Ait-Ameur. "A New Class of $$L^2$$-Stable Schemes for the Isentropic Euler Equations on Staggered Grids." In Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_39.

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Waśkiewicz, Kamil, and Wojciech Dębski. "Time Scales: Towards Extending the Finite Difference Technique for Non-homogeneous Grids." In Achievements, History and Challenges in Geophysics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07599-0_22.

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Hemker, P. W., and F. Sprengel. "Experience with the Solution of a Finite Difference Discretization in Sparse Grids." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45262-1_47.

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Hokpunna, Arpiruk, and Michael Manhart. "Compact Fourth-Order Finite-Volume Method for Numerical Solutions of Navier–Stokes Equations on Staggered Grids." In Direct and Large-Eddy Simulation VII. Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3652-0_19.

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Conference papers on the topic "Staggered grids finite difference"

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Xia, Z. Z., P. Zhang, and R. Z. Wang. "A Novel Finite Difference Method for Flow Calculation on Colocated Grids." 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/ht2008-56265.

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Abstract:
A new finite difference method, which removes the need for staggered grids in fluid dynamic computation, is presented. Pressure checker boarding is prevented through a dual-velocity scheme that incorporates the influence of pressure on velocity gradients. A supplementary velocity resulting from the discrete divergence of pressure gradient, together with the main velocity driven by the discretized pressure first-order gradient, is introduced for the discretization of continuity equation. The method in which linear algebraic equations are solved using incomplete LU factorization, removes the pressure-correction equation, and was applied to rectangle duct flow and natural convection in a cubic cavity. These numerical solutions are in excellent agreement with the analytical solutions and those of the algorithm on staggered grids. The new method is shown to be superior in convergence compared to the original one on staggered grids.
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Igel, Heiner, Bruno Riollet, and Peter Mora. "Accuracy of staggered 3‐D finite‐difference grids for anisotropic wave propagation." In SEG Technical Program Expanded Abstracts 1992. Society of Exploration Geophysicists, 1992. http://dx.doi.org/10.1190/1.1821960.

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O'Reilly, Ossian, Tomas Lundquist, and Jan Nordström. "ENERGY STABLE HIGH ORDER FINITE DIFFERENCE METHODS ON STAGGERED GRIDS: AN INITIAL INVESTIGATION." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2027.11578.

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Trenchant, Vincent, Hector Ramirez, Yann Le Gorrec, and Paul Kotyczka. "Structure preserving spatial discretization of 2D hyperbolic systems using staggered grids finite difference." In 2017 American Control Conference (ACC). IEEE, 2017. http://dx.doi.org/10.23919/acc.2017.7963327.

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Saenger, E. H., and T. Bohlen. "Viscoelastic Finite-Difference Modeling Using the Rotated Staggered Grid." In 64th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2002. http://dx.doi.org/10.3997/2214-4609-pdb.5.c025.

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Yong, P., J. P. Huang, Z. C. Li, L. P. Qu, and Q. Y. Li. "Optimized Equivalent Staggered Grid Finite Difference for Acoustic Modeling." In 78th EAGE Conference and Exhibition 2016. EAGE Publications BV, 2016. http://dx.doi.org/10.3997/2214-4609.201601172.

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Jiang*, Fan, and Shengwen Hin. "Hybrid Viscoelastic Modeling with Adaptive Finite Difference Staggered Grid." In Beijing 2014 International Geophysical Conference & Exposition, Beijing, China, 21-24 April 2014. Society of Exploration Geophysicists and Chinese Petroleum Society, 2014. http://dx.doi.org/10.1190/igcbeijing2014-175.

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Chen*, Hanming, Hui Zhou, Qingchen Zhang, and Qi Zhang. "Optimized time-space domain staggered-grid finite-difference methods based on new finite-difference stencils." In SEG Technical Program Expanded Abstracts 2015. Society of Exploration Geophysicists, 2015. http://dx.doi.org/10.1190/segam2015-5797871.1.

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Saenger, E. H., and T. Bohlen. "Accurate Anisotropic Finite-Difference Modeling Using the Rotated Staggered Grid." In 65th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2003. http://dx.doi.org/10.3997/2214-4609-pdb.6.p011.

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Chen, How‐Wei, Tai‐Min Huang, Min‐Hsiung, and Chia Yi. "Time‐domain staggered‐grid finite‐difference simulation of GPR data." In SEG Technical Program Expanded Abstracts 1996. Society of Exploration Geophysicists, 1996. http://dx.doi.org/10.1190/1.1826772.

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Reports on the topic "Staggered grids finite difference"

1

Aldridge, David Franklin, Sandra L. Collier, David H. Marlin, Vladimir E. Ostashev, Neill Phillip Symons, and D. Keith Wilson. Staggered-grid finite-difference acoustic modeling with the Time-Domain Atmospheric Acoustic Propagation Suite (TDAAPS). Office of Scientific and Technical Information (OSTI), 2005. http://dx.doi.org/10.2172/966592.

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Kuo, Hung-Chi. Tests of Various Finite Difference Algorithms Applied to a Simple Water Vapor Transport Problem on a Staggered Grid. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada210229.

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Sjogreen, B., H. Yee, and M. Vinokur. On High Order Finite-Difference Metric Discretizations Satisfying GCL on Moving and Deforming Grids. Office of Scientific and Technical Information (OSTI), 2013. http://dx.doi.org/10.2172/1084713.

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