Relevant bibliographies by topics / Advection-Dominated problems

Academic literature on the topic 'Advection-Dominated problems'

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Published: 13 April 2024

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Journal articles on the topic "Advection-Dominated problems"

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Abgrall, Rémi, and Arnaud Krust. "An adaptive enrichment algorithm for advection-dominated problems." International Journal for Numerical Methods in Fluids 72, no. 3 (November 9, 2012): 359–74. http://dx.doi.org/10.1002/fld.3745.

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Chen, Zhangxin, So-Hsiang Chou, and Do Young Kwak. "Characteristic-mixed covolume methods for advection-dominated diffusion problems." Numerical Linear Algebra with Applications 13, no. 9 (2006): 677–97. http://dx.doi.org/10.1002/nla.492.

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Park, Nam-Sik, and James A. Liggett. "Taylor-least-squares finite element for two-dimensional advection-dominated unsteady advection-diffusion problems." International Journal for Numerical Methods in Fluids 11, no. 1 (July 5, 1990): 21–38. http://dx.doi.org/10.1002/fld.1650110103.

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Lee, J. H. W., J. Peraire, and O. C. Zienkiewicz. "The characteristic-Galerkin method for advection-dominated problems—An assessment." Computer Methods in Applied Mechanics and Engineering 61, no. 3 (April 1987): 359–69. http://dx.doi.org/10.1016/0045-7825(87)90100-9.

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Brezzi, F., G. Gazzaniga, and L. D. Marini. "A preconditioner for domain decomposition methods for advection-dominated problems." Transport Theory and Statistical Physics 25, no. 3-5 (April 1996): 555–65. http://dx.doi.org/10.1080/00411459608220721.

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Chen, Zhangxin. "Characteristic-nonconforming finite-element methods for advection-dominated diffusion problems." Computers & Mathematics with Applications 48, no. 7-8 (October 2004): 1087–100. http://dx.doi.org/10.1016/j.camwa.2004.10.007.

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Lube, Gert, and Gerd Rapin. "Residual-based stabilized higher-order FEM for advection-dominated problems." Computer Methods in Applied Mechanics and Engineering 195, no. 33-36 (July 2006): 4124–38. http://dx.doi.org/10.1016/j.cma.2005.07.017.

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Pilatti, Cristiana, Bárbara Denicol do Amaral Rodriguez, and João Francisco Prolo Filho. "Performance Analysis of Stehfest and Power Series Expansion Methods for Solution to Diffusive and Advective Transport Problems." Defect and Diffusion Forum 396 (August 2019): 99–108. http://dx.doi.org/10.4028/www.scientific.net/ddf.396.99.

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This paper presents results of the test of methods for numerical inversion of the Laplace Transform for solving the one-dimensional advection-diffusion equation, which describes solute transport processes, focusing on the contaminant transport in a porous medium. The performance of Stehfest and Power Series Expansion methods is analyzed, for diffusion-dominated and advection-dominated transport problems under linear flow condition. Numerical results are compared to the analytical solution by means of the absolute error. Based on these results, we concluded that both methods, Stehfest and Power Series Expansion, are recommended only for diffusion-dominated cases.
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Shilt, Troy, Patrick J. O’Hara, and Jack J. McNamara. "Stabilization of advection dominated problems through a generalized finite element method." Computer Methods in Applied Mechanics and Engineering 383 (September 2021): 113889. http://dx.doi.org/10.1016/j.cma.2021.113889.

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Chen, Peng, Alfio Quarteroni, and Gianluigi Rozza. "Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations." SIAM Journal on Numerical Analysis 51, no. 5 (January 2013): 2700–2722. http://dx.doi.org/10.1137/120884158.

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Dissertations / Theses on the topic "Advection-Dominated problems"

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Biezemans, Rutger. "Multiscale methods : non-intrusive implementation, advection-dominated problems and related topics." Electronic Thesis or Diss., Marne-la-vallée, ENPC, 2023. http://www.theses.fr/2023ENPC0029.

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Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) multi-échelles, et en particulier sur la méthode dite des éléments finis multi-échelles (MsFEM). Celle-ci est une méthode de type éléments finis qui consiste en une approximation de Galerkin de l'EDP sur une base problème-dépendante. Trois difficultés particulières liées à cette méthode sont abordées dans cette thèse. Premièrement, puisque la MsFEM utilise une base problème-dépendante, la méthode ne peut être facilement implémentée dans des codes industriels génériques. Cela freine la diffusion de la MsFEM au-delà des environnements académiques. Une méthodologie générique est proposée pour convertir la MsFEM en un problème effectif qui peut être résolu par des codes génériques. Il est démontré par des résultats théoriques ainsi que des expériences numériques que la nouvelle méthodologie est aussi précise que la MsFEM originale. Deuxièmement, les MsFEM adaptées aux problèmes advection-dominés sont étudiées. Ce régime spécifique rend instables les discrétisations naïves. Une explication est trouvée pour l'instabilité de certaines méthodes proposées précédemment. Des expériences numériques montrent la stabilité d'une MsFEM avec des conditions aux limites de type Crouzeix-Raviart enrichie par des fonctions bulles. Troisièmement, une nouvelle analyse de convergence pour la MsFEM est présentée, permettant pour la première fois d'établir la convergence sous des hypothèses de régularité minimales. Cette démarche est importante pour réduire l'écart entre la théorie pour la MsFEM et son application en pratique, où les hypothèses de régularité habituelles sont rarement satisfaites
This thesis is concerned with computational methods for multiscale partial differential equations (PDEs), and in particular the multiscale finite element method (MsFEM). This is a finite element type method that performs a Galerkin approximation of the PDE on a problem-dependent basis. Three particular difficulties related to the method are addressed in this thesis. First, the intrusiveness of the MsFEM is considered. Since the MsFEM uses a problem-dependent basis, it cannot easily be implemented in generic industrial codes and this hinders its adoption beyond academic environments. A generic methodology is proposed that translates the MsFEM into an effective problem that can be solved by generic codes. It is shown by theoretical convergence estimates and numerical experiments that the new methodology is as accurate as the original MsFEM. Second, MsFEMs for advection-dominated problems are studied. These problems cause additional instabilities for naive discretizations. An explanation is found for the instability of previously proposed methods. Numerical experiments show the stability of an MsFEM with Crouzeix-Raviart type boundary conditions enriched with bubble functions. Third, a new convergence analysis for the MsFEM is presented that, for the first time, establishes convergence under minimal regularity hypotheses. This bridges an important gap between the theoretical understanding of the method and its field of application, where the usual regularity hypotheses are rarely satisfied
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Hunt, David Patrick. "Mesh-free radial basis function methods for advection-dominated diffusion problems." Thesis, University of Leicester, 2005. http://hdl.handle.net/2381/30529.

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This thesis is concerned with the numerical solution of advection-dominated diffusion problems. There are essentially two key aspects to this work: the derivatives of an a priori error estimate for a semi-Lagrangian mesh-free method using radial basis function interpolation to numerically approximate the first-order linear transport problem; and the design and testing of a semi-Lagrangian mesh-less method to numerically solve the full parabolic advection-diffusion problem, using radial basis function Hermite interpolation. We begin by establishing the theory of radical basis function interpolation, including new results for the stability of interpolation via the class of radial basis functions known as polyharmonic splines, as well as error estimates for interpolation by the same class of function. These results provide us with the necessary tools to prove the a priori error estimate for the semi-Lagrangian advection scheme, given certain assumptions on the smoothness of the solution. We then validate both the scheme and the analysis with a series of numerical experiments. By introducing the concept of Hermite interpolation, we develop and implement a new semi-Lagrangian method for the numerical approximation of advection-dominated diffusion problems, which is validated through two numerical experiments.
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Book chapters on the topic "Advection-Dominated problems"

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Sun, Ne-Zheng. "Numerical Solutions of Advection-Dominated Problems." In Mathematical Modeling of Groundwater Pollution, 149–86. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-2558-2_6.

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van der Ploeg, Auke, Rony Keppens, and Gábor Tóth. "Block incomplete LU-preconditioners for implicit solution of advection dominated problems." In High-Performance Computing and Networking, 421–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0031614.

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Griebel, Michael, Christian Rieger, and Alexander Schier. "Upwind Schemes for Scalar Advection-Dominated Problems in the Discrete Exterior Calculus." In Transport Processes at Fluidic Interfaces, 145–75. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56602-3_6.

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Bicol, Kayla, and Annalisa Quaini. "On the Sensitivity to Model Parameters in a Filter Stabilization Technique for Advection Dominated Advection-Diffusion-Reaction Problems." In Lecture Notes in Computational Science and Engineering, 131–43. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-30705-9_12.

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"6. Advection-Dominated Problems." In Mathematical Modeling of Earth's Dynamical Systems, 111–29. Princeton: Princeton University Press, 2011. http://dx.doi.org/10.1515/9781400839117.111.

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"test problems real features of environmental in advection-dominated transport." In Hydraulic Engineering Software IV, 135–38. CRC Press, 2003. http://dx.doi.org/10.1201/9781482286809-44.

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Conference papers on the topic "Advection-Dominated problems"

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Chen, Leitao, Timothy Petrosius, and Laura Schaefer. "Numerical Simulation of Heat Conduction Problems With the Lattice Boltzmann Method (LBM) and Discrete Boltzmann Method (DBM): A Comparative Study." In ASME 2020 Heat Transfer Summer Conference collocated with the ASME 2020 Fluids Engineering Division Summer Meeting and the ASME 2020 18th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/ht2020-8972.

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Abstract Unlike Fourier’s law, which is built upon the continuum assumption and constitutive equation of energy conservation, kinetic models study the transport phenomena from a more fundamental level and in a more generalized way. The Boltzmann equation (BE), which is one type of kinetic model, is a generalized transport model that can solve any advection-diffusion problem regardless of whether such a problem is advection-dominated or diffusion-dominated. Although the BE has been successfully applied to model fluid transport, which is an advection-dominated process, in this paper, in order to demonstrate the generality of the BE, heat conduction, which is a diffusion-only process, is simulated by two numerical derivatives of the BE: the lattice Boltzmann method (LBM) and the discrete Boltzmann method (DBM). The DBM model presented in this paper is unique in the way that the BE is solved on complete unstructured grids with the finite volume method. Therefore, it is named the finite volume discrete Boltzmann method (FVDBM). Two two-dimensional heat conduction problems with different domain geometries and boundary conditions are simulated by both the LBM and FVDBM and quantitatively compared. From that comparison, it is found that the FVDBM produces a higher level of accuracy than the LBM for problems with curved boundaries, while maintaining the same accuracy as the LBM for problems with straight boundaries. The advantage displayed by the FVDBM approach is the direct result of a more accurate reconstruction of curved boundaries by the utilization of unstructured grids, versus the Cartesian grids necessary for the LBM.
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Lu, Qiyue, and Shiyi Bao. "A Finite Element Approach to Solve Incompressible Navier-Stokes Equations and Its Convergence Rate Analysis." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-88982.

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Abstract Finite element methods for fluid flow problems are gaining more interests in nuclear engineering fields in recent years. Based on linear triangle elements, this work implements the algebraic subgrid scale (ASGS) stabilized finite element model for solving advection dominated incompressible fluid flows. The non-linearity is handled by the fixed point iteration. Verification is carried out using the method of manufactured solutions (MMS) for convergence rate analysis and the unit square lid-driven cavity benchmark problem.
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Chao, Shih-hui, Mark R. Holl, John H. Koschwanez, Pahnit Seriburi, and Deirdre R. Meldrum. "Scaling for Microfluidic Mixing." In ASME 3rd International Conference on Microchannels and Minichannels. ASMEDC, 2005. http://dx.doi.org/10.1115/icmm2005-75236.

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Mixing in microfluidic channels or chambers is typically dominated by molecular diffusion. A common method used to evaluate mixing involves the examination of a time series of instantaneous concentration maps of fluid tracers (colorimetric or fluorescent) that enable visualization of fluid layering and simultaneous diffusive mixing. A scale often used to characterize micromixer performance is the global deviation of these concentration maps. While useful, this measurement scale does not provide a sensitive metric for evaluating fluid layering in the mixing process. This paper proposes an analytical approach that examines spatial concentration gradients and a global gradient-based scale, a normalized L2 norm of the gradient map, for micromixer performance evaluation. This gradient-based scale is complementary to deviation-based scales and is especially useful for the class of micromixers that enhance mixing by stretching and folding of fluids, whether the dominant mode of mixing is diffusion or chaotic advection. The algorithm is easy for micromixer designers to implement and will reveal performance metric information that remains implicitly hidden when deviation-based scales are used. The use of gradient-based mixing performance evaluation is illustrated with baker’s transform, a series of discrete mappings similar to kneading dough. The changes in both the deviation-based and gradient-based scale created by discrete fluid stretching and folding are discussed. The results from the one-dimensional discrete mixing problem are extended to a realistic mixing problem that simulates continuous stretching and folding.
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