Relevant bibliographies by topics / Glimm scheme

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Glimm scheme'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Glimm scheme"

1

Bianchini, Stefano, and Stefano Modena. "On a quadratic functional for scalar conservation laws." Journal of Hyperbolic Differential Equations 11, no. 02 (June 2014): 355–435. http://dx.doi.org/10.1142/s0219891614500118.

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We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme. The proof is based on the introduction of a quadratic functional 𝔔(t), decreasing at every interaction, and such that its total variation in time is bounded. Differently from other interaction potentials present in the literature, the form of this functional is the natural extension of the original Glimm functional, and coincides with it in the genuinely nonlinear case.
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Bressan, Alberto. "The unique limit of the Glimm scheme." Archive for Rational Mechanics and Analysis 130, no. 3 (1995): 205–30. http://dx.doi.org/10.1007/bf00392027.

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HUA, JIALE, and TONG YANG. "A NOTE ON THE NEW GLIMM FUNCTIONAL FOR GENERAL SYSTEMS OF HYPERBOLIC CONSERVATION LAWS." Mathematical Models and Methods in Applied Sciences 20, no. 05 (May 2010): 815–42. http://dx.doi.org/10.1142/s0218202510004453.

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For systems of hyperbolic conservation laws, a new Glimm functional was recently constructed when the linearly degenerate manifold in each characteristic field is either the whole space or it consists of a finitely many smooth and transversal manifolds of codimension one. This new functional leads to the neat consistency and convergence rate estimation of the Glimm scheme. In this paper, by the motivation of the result in Ref. 2, we show that the corresponding new Glimm functional can be constructed for general systems only under the strict hyperbolicity assumption.
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Frid, Hermano. "Periodic solutions of conservation laws constructed through Glimm scheme." Transactions of the American Mathematical Society 353, no. 11 (June 1, 2001): 4529–44. http://dx.doi.org/10.1090/s0002-9947-01-02813-6.

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Wang, Zejun, and Qi Zhang. "Periodic solutions to p-system constructed through Glimm scheme." Journal of Mathematical Analysis and Applications 435, no. 2 (March 2016): 1088–98. http://dx.doi.org/10.1016/j.jmaa.2015.10.070.

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Ancona, Fabio, and Andrea Marson. "A Locally Quadratic Glimm Functional and Sharp Convergence Rate of the Glimm Scheme for Nonlinear Hyperbolic Systems." Archive for Rational Mechanics and Analysis 196, no. 2 (July 2, 2009): 455–87. http://dx.doi.org/10.1007/s00205-009-0248-3.

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Hua, Jiale, Zaihong Jiang, and Tong Yang. "A New Glimm Functional and Convergence Rate of Glimm Scheme for General Systems of Hyperbolic Conservation Laws." Archive for Rational Mechanics and Analysis 196, no. 2 (September 19, 2009): 433–54. http://dx.doi.org/10.1007/s00205-009-0266-1.

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Chou, Shih-Wei, John M. Hong, Bo-Chih Huang, and Reyna Quita. "Global bounded variation solutions describing Fanno–Rayleigh fluid flows in nozzles." Mathematical Models and Methods in Applied Sciences 28, no. 06 (May 21, 2018): 1135–69. http://dx.doi.org/10.1142/s0218202518500306.

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In this paper, we investigate the initial-boundary value problem of compressible Euler equations including friction and heating that model the transonic Fanno–Rayleigh flows through symmetric variable area nozzles. In particular, the case of contracting nozzles is considered. A new version of a generalized Glimm scheme (GGS) is presented for establishing the global existence of entropy solutions with bounded variation. Modified Riemann and boundary Riemann solutions are applied to design this GGS, which is constructed using the contraction matrices acting on the homogeneous Riemann (or boundary-Riemann) solutions. The extended Glimm–Goodman’s type of wave interaction estimates are investigated to determine the stability of the scheme and the positivity of gas velocity that results in the existence of the weak solution. The limit of approximation solutions serves as an entropy solution. Moreover, a quantitative relation between the shape of the nozzle, friction, and heat is proposed for the global existence result in the contracting nozzle. Numerical simulations of the contraction-expansion and expansion-contraction nozzles are presented to validate the scheme.
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Bressan, Alberto, and Andrea Marson. "Error Bounds for a Deterministic Version of the Glimm Scheme." Archive for Rational Mechanics and Analysis 142, no. 2 (May 1, 1998): 155–76. http://dx.doi.org/10.1007/s002050050088.

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Gremaud, Pierre A., and Yi Sun. "Numerical Study of Singularity Formation in Relativistic Euler Flows." Communications in Computational Physics 16, no. 2 (August 2014): 348–64. http://dx.doi.org/10.4208/cicp.221212.300114a.

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AbstractThe formation of singularities in relativistic flows is not well understood. Smooth solutions to the relativistic Euler equations are known to have a finite lifespan; the possible breakdown mechanisms are shock formation, violation of the subluminal conditions and mass concentration. We propose a new hybrid Glimm/central-upwind scheme for relativistic flows. The scheme is used to numerically investigate, for a family of problems, which of the above mechanisms is involved.
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Dissertations / Theses on the topic "Glimm scheme"

1

Dongmo, Nguepi Guissel Lagnol. "Modèles mathématiques et numériques avancés pour la simulation du polymère dans les réservoirs pétroliers." Electronic Thesis or Diss., université Paris-Saclay, 2021. http://www.theses.fr/2021UPASG077.

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Une technique efficace pour accroître la production d’un champ pétrolier consiste à y injecter un mélange d’eau et de polymère. La viscosité du polymère réduit en effet la mobilité de l’eau, qui pousse alors mieux l’huile, d’où un taux d’extraction plus élevé. La simulation numérique d’un tel procédé de récupération d’hydrocarbures revêt donc d’une importance capitale. Or, malgré des décennies de recherche, la modélisation des écoulements avec polymère en milieu poreux et sa résolution numérique demeurent un sujet difficile. D’une part, les modèles habituellement employés par les ingénieurs de réservoir présentent, au mieux, des singularités de type résonance qui les rend faiblement hyperboliques. Ce défaut donne lieu à certaines complicationsD’une part, les modèles habituellement employés par les ingénieurs de réservoir présentent, au mieux, des singularités de type résonance qui les rend faiblement hyperboliques. Ce défaut donne lieu à certaines complications mais reste acceptable. Au pire, quand on veut incorporer l’effet du volume de pore inaccessible (IPV), les modèles deviennent non hyperboliques, ce qui aggrave les instabilités numériques susceptibles d’apparaître.D’autre part, les schémas numériques classiques ne conduisent pas à des résultats satisfaisants. Sans IPV, la diffusion excessive autour de l’onde de contact fait perdre les informations pertinentes. Avec IPV, l’existence des valeurs propres complexes crée des instabilités exponentielles au niveau continu qu’il faut traiter au niveau discret sous peine d’arrêt prématuré du code.L’objectif de cette thèse est de remédier à ces difficultés. Au niveau des modèles, nous analysons plusieurs lois d’IPV et établissons une équivalence entre deux d’entre elles. Nous proposons de surcroît des conditions suffisantes raisonnables sur la loi d’IPV en vue de l’hyperbolicité faible du système d’écoulement. Au niveau des schémas pour le problème sans IPV, nous préconisons une correction afin d’améliorer la précision des discontinuités de contact. Pour le problème avec IPV,nous élaborons une méthode de relaxation qui garantit la stabilité des calculs quelle que soit la loi IPV
An effective technique to increase production in an oil field is to inject a mixture of water and polymer. The viscosity of polymer reduces the mobility of water, which then pushes oil better, resulting in a higher extraction rate. The numerical simulation of such an enhanced oil recovery is therefore of paramount importance. However, despite decades of research, the modeling of polymer flows in porous media and its numerical resolution remains a difficult subject.On the one hand, the models traditionally used by reservoir engineers exhibit, in the best case, resonance-like singularities that make them weakly hyperbolic. Thisdefect gives rise to some complications but remains acceptable. In the worst case, when we wish to incorporate the effect of the inaccessible pore volume (IPV), themodels become non-hyperbolic, which exacerbates the numerical instabilities that are likely to appear.On the other hand, classical numerical schemes do not yield satisfactory results. Without IPV, the excessive diffusion around the contact wave causes the most relevant information to be lost. With IPV, the existence of complex eigenvalues generates exponential instabilities at the continuous level that must be addressed at the discrete level to avoid a premature stop of the code.The objective of this thesis is to remedy these difficulties. Regarding models, we analyze several IPV laws and show an equivalence between two of them. Furthermore, we propose reasonable sufficient conditions on the IPV law to enforce weak hyperbolicity of the flow system. Regarding schemes for the problem without IPV, we advocate a correction to improve the accuracy of contact discontinuities. For the problem with IPV, we design a relaxation method that guarantees the stability of the calculations for all IPV laws
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Books on the topic "Glimm scheme"

1

Groah, Jeffrey, Blake Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes. Springer London, Limited, 2007.

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Groah, Jeffrey, Blake Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes. Springer, 2010.

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Groah, Jeffrey, B. Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes (Springer Monographs in Mathematics). Springer, 2006.

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Shock-Wave Solutions Of The Einstein Equations With Perfect Fluid Sources: Existence And Consistency By A Locally Inertial Glimm Scheme (Memoirs of the American Mathematical Society). American Mathematical Society, 2004.

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Book chapters on the topic "Glimm scheme"

1

Smoller, Joel. "The Glimm Difference Scheme." In Grundlehren der mathematischen Wissenschaften, 368–90. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0873-0_19.

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2

"The Glimm scheme." In Systems of Conservation Laws 1, 146–85. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9780511612374.006.

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"5. Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme." In Vanishing Viscosity Method, 485–530. De Gruyter, 2016. http://dx.doi.org/10.1515/9783110494273-005.

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Aitkin, Murray, Brain Francis, and John Hinde. "Introducing GLIM4." In Statistical Modelling in GLIM 4, 1–24. Oxford University PressOxford, 2005. http://dx.doi.org/10.1093/oso/9780198524137.003.0001.

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Abstract Statistical modelling is an iterative process. We have a research question of interest, the experimental or observational context, the sampling scheme and the data. Based on these data and the other information, we develop an initial model, fit it to the data and examine the model output. We then plot the residuals, check the model assumptions and examine the parameter estimates. Based on this model output, we may modify the first model possibly through some transformation or the addition or subtraction of model terms. Fitting the second model may in turn lead to further models for the data, with the form of the current model being based on the information provided by the previous models. This interactivitybetween the data and the data modeller is a crucial feature of the process of statistical modelling. While automatic model selection procedures provided in many software packages can provide guidance in large problems, we take a different route in this book.
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Swan, Tony, Robert Gilchrist, Malcolm Bradley, Mike Clarke, Peter Green, Allan Reese, John Hinde, Andrew Stalewski, and Carl O’brien. "Applications of GLIM." In The Glim System, 306–622. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198522317.003.0014.

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Abstract This chapter of the Modelling Guide is intended to give a set of more or less complete analyses covering a range of practical problems for which GLIM is useful. The examples are also intended to convey how the various facilities of GLIM, especially the high-resolution graphics, may be used with practical problems, and to provide a useful reference for users with similar problems. The examples given here are designed to cover the most common problems that arise for which univariate modelling is appropriate. They are grouped, mainly, according to the type of response variable of which the main types of interest are continuous (measured), dichotomous (two categories), and counted (frequencies). However there is some overlap so it was not possible to keep rigidly to this scheme.
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Conference papers on the topic "Glimm scheme"

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Cunha da Silva, Daniel, Maria Laura Martins-Costa, and ROGERIO GAMA. "APPLICATION OF GLIMM SCHEME FOR DESCRIBING FLOW THROUGH POROUS MEDIA WITH KINEMATICAL CONSTRAINED FLUID FRACTION." In 18th Brazilian Congress of Thermal Sciences and Engineering. ABCM, 2020. http://dx.doi.org/10.26678/abcm.encit2020.cit20-0233.

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Dongmo, G., B. Braconnier, C. Preux, Q. Tran, and C. Berthon. "Glimm and Finite Volume Schemes for Polymer Flooding Model with and Without Inaccessible Pore Volume Law." In ECMOR XVII. European Association of Geoscientists & Engineers, 2020. http://dx.doi.org/10.3997/2214-4609.202035090.

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You might also be interested in the extended bibliographies on the topic 'Glimm scheme' for particular source types:
Journal articles
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