Relevant bibliographies by topics / Advection-diffusion equation

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Academic literature on the topic 'Advection-diffusion equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Advection-diffusion equation"

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Gautam, Pushpa Nidhi, Buddhi Prasad Sapkota, and Kedar Nath Uprety. "A brief review on the solutions of advection-diffusion equation." Scientific World 15, no. 15 (June 14, 2022): 4–9. http://dx.doi.org/10.3126/sw.v15i15.45668.

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In this work both linear and nonlinear advection-diffusion equations are considered and discussed their analytical solutions with different initial and boundary conditions. The work of Ogata and Banks, Harleman and Rumer, Cleary and Adrian, Atul Kumar et al., Mojtabi and Deville are reviewed for linear advection-diffusion equations and for nonlinear, we have chosen the work of Sakai and Kimura. Some enthusiastic functions used in the articles, drawbacks and applications of the results are discussed. Reduction of the advection-diffusion equations into diffusion equations make the governing equation solvable by using integral transform method for analytical solution. For nonlinear advection-diffusion equations, the Cole-Hopf transformation is used to reduce into the diffusion equation. Different dispersion phenomena in atmosphere, surface and subsurface area are outlined.
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Hadadian Nejad Yousefi, Mohsen, Seyed Hossein Ghoreishi Najafabadi, and Emran Tohidi. "A new spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations via Chebyshev polynomials." Engineering Computations 36, no. 7 (August 12, 2019): 2327–68. http://dx.doi.org/10.1108/ec-02-2018-0063.

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Purpose The purpose of this paper is to develop an efficient and reliable spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations. Design/methodology/approach In this study, the considered two-dimensional unsteady advection-diffusion equations are transformed into the equivalent partial integro-differential equations via integrating from the considered unsteady advection-diffusion equation. After this stage, by using Chebyshev polynomials of the first kind and the operational matrix of integration, the integral equation would be transformed into the system of linear algebraic equations. Robustness and efficiency of the proposed method were illustrated by six numerical simulations experimentally. The numerical results confirm that the method is efficient, highly accurate, fast and stable for solving two-dimensional unsteady advection-diffusion equations. Findings The proposed method can solve the equations with discontinuity near the boundaries, the advection-dominated equations and the equations in irregular domains. One of the numerical test problems designed specially to evaluate the performance of the proposed method for discontinuity near boundaries. Originality/value This study extends the intention of one dimensional Chebyshev approximate approaches (Yuksel and Sezer, 2013; Yuksel et al., 2015) for two-dimensional unsteady advection-diffusion problems and the basic intention of our suggested method is quite different from the approaches for hyperbolic problems (Bulbul and Sezer, 2011).
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Sene, Ndolane, and Karima Abdelmalek. "Nonlinear sub-diffusion and nonlinear sub-diffusion dispersion equations and their proposed solutions." Applied Mathematics and Nonlinear Sciences 5, no. 1 (March 31, 2020): 221–36. http://dx.doi.org/10.2478/amns.2020.1.00020.

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AbstractMany investigations related to the analytical solutions of the nonlinear sub-diffusion equation exist. In this paper, we investigate the conditions under which the analytical and the approximate solutions of the nonlinear sub-diffusion equation and the nonlinear sub-advection dispersion equation exist. In other words, the problems of existence and uniqueness of the solutions the fractional diffusion equations have been addressed. We use the Banach fixed Theorem. After proving the existence and uniqueness, we propose the analytical and the approximate solutions of the nonlinear sub-diffusion, and the nonlinear sub-advection dispersion equations. We analyze the impact of the sub-diffusion coefficient, the advection coefficient and the dispersion coefficient in the diffusion processes. The homotopy perturbation Laplace transform method has been used in this paper. Some numerical examples are provided to illustrate the main results of the article.
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Chang Fu-Xuan, Chen Jin, and Huang Wei. "Anomalous diffusion and fractional advection-diffusion equation." Acta Physica Sinica 54, no. 3 (2005): 1113. http://dx.doi.org/10.7498/aps.54.1113.

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Avci, Derya, Eroğlu İskender, and Necati Özdemir. "The Dirichlet problem of a conformable advection-diffusion equation." Thermal Science 21, no. 1 Part A (2017): 9–18. http://dx.doi.org/10.2298/tsci160421235a.

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The fractional advection-diffusion equations are obtained from a fractional power law for the matter flux. Diffusion processes in special types of porous media which has fractal geometry can be modelled accurately by using these equations. However, the existing nonlocal fractional derivatives seem complicated and also lose some basic properties satisfied by usual derivatives. For these reasons, local fractional calculus has recently been emerged to simplify the complexities of fractional models defined by nonlocal fractional operators. In this work, the conformable, a local, well-behaved and limit-based definition, is used to obtain a local generalized form of advection-diffusion equation. In addition, this study is devoted to give a local generalized description to the combination of diffusive flux governed by Fick?s law and the advection flux associated with the velocity field. As a result, the constitutive conformable advection-diffusion equation can be easily achieved. A Dirichlet problem for conformable advection-diffusion equation is derived by applying fractional Laplace transform with respect to time t and finite sin-Fourier transform with respect to spatial coordinate x. Two illustrative examples are presented to show the behaviours of this new local generalized model. The dependence of the solution on the fractional order of conformable derivative and the changing values of problem parameters are validated using graphics held by MATLcodes.
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Wu, Jiankang. "Wave equation model for solving advection-diffusion equation." International Journal for Numerical Methods in Engineering 37, no. 16 (August 30, 1994): 2717–33. http://dx.doi.org/10.1002/nme.1620371603.

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Dhawan, S., and S. Kapoor. "Numerical simulation of advection-diffusion equation." International Journal of Mathematical Modelling and Numerical Optimisation 2, no. 1 (2011): 13. http://dx.doi.org/10.1504/ijmmno.2011.037197.

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Grant, John, and Michael Wilkinson. "Advection–Diffusion Equation with Absorbing Boundary." Journal of Statistical Physics 160, no. 3 (April 30, 2015): 622–35. http://dx.doi.org/10.1007/s10955-015-1257-2.

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CANUTO, C., and A. RUSSO. "ON THE ELLIPTIC-HYPERBOLIC COUPLING I: THE ADVECTION-DIFFUSION EQUATION VIA THE χ-FORMULATION." Mathematical Models and Methods in Applied Sciences 03, no. 02 (April 1993): 145–70. http://dx.doi.org/10.1142/s0218202593000096.

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An advection-diffusion equation is considered, for which the solution is advection-dominated in most of the domain. A domain decomposition method based on a self-adaptive, smooth coupling of the reduced advection equation and the full advection-diffusion equation is proposed. The convergence of an iteration-by-subdomain method is investigated.
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Appadu, Appanah Rao. "Performance of UPFD scheme under some different regimes of advection, diffusion and reaction." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 7 (July 3, 2017): 1412–29. http://dx.doi.org/10.1108/hff-01-2016-0038.

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Purpose An unconditionally positive definite finite difference scheme termed as UPFD has been derived to approximate a linear advection-diffusion-reaction equation which models exponential travelling waves and the coefficients of advection, diffusion and reactive terms have been chosen as one (Chen-Charpentier and Kojouharov, 2013). In this work, the author tests UPFD scheme under some other different regimes of advection, diffusion and reaction. The author considers the case when the coefficient of advection, diffusion and reaction are all equal to one and also cases under which advection or diffusion or reaction is more important. Some errors such as L1 error, dispersion, dissipation errors and relative errors are tabulated. Moreover, the author compares some spectral properties of the method under different regimes. The author obtains the variation of the following quantities with respect to the phase angle: modulus of exact amplification factor, modulus of amplification factor of the scheme and relative phase error. Design/methodology/approach Difficulties can arise in stability analysis. It is important to have a full understanding of whether the conditions obtained for stability are sufficient, necessary or necessary and sufficient. The advection-diffusion-reaction is quite similar to the advection-diffusion equation, it has an extra reaction term and therefore obtaining stability of numerical methods discretizing advection-diffusion-reaction equation is not easy as is the case with numerical methods discretizing advection-diffusion equations. To avoid difficulty involved with obtaining region of stability, the author shall consider unconditionally stable finite difference schemes discretizing advection-diffusion-reaction equations. Findings The UPFD scheme is unconditionally stable but not unconditionally consistent. The scheme was tested on an advection-diffusion-reaction equation which models exponential travelling waves, and the author computed various errors such as L1 error, dispersion and dissipation errors, relative errors under some different regimes of advection, diffusion and reaction. The scheme works best for very small values of k as k → 0 (for instance, k = 0.00025, 0.0005) and performs satisfactorily at other values of k such as 0.001 for two regimes; a = 1, D = 1, κ = 1 and a = 1, D = 1, κ = 5. When a = 5, D = 1, κ = 1, the scheme performs quite well at k = 0.00025 and satisfactorily at k = 0.0005 but is not efficient at larger values of k. For the diffusive case (a = 1, D = 5, κ = 1), the scheme does not perform well. In general, the author can conclude that the choice of k is very important, as it affects to a great extent the performance of the method. Originality/value The UPFD scheme is effective to solve advection-diffusion-reaction problems when advection or reactive regime is dominant and for the case, a = 1, D = 1, κ = 1, especially at low values of k. Moreover, the magnitude of the dispersion and dissipation errors using UPFD are of the same order for all the four regimes considered as seen from Tables 1 to 4. This indicates that if the author is to optimize the temporal step size at a given value of the spatial step size, the optimization function must consist of both the AFM and RPE. Some related work on optimization can be seen in Appadu (2013). Higher-order unconditionally stable schemes can be constructed for the regimes for which UPFD is not efficient enough for instance when advection and diffusion are dominant.
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Dissertations / Theses on the topic "Advection-diffusion equation"

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Molkenthin, Nora. "Advection-diffusion-networks." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2014. http://dx.doi.org/10.18452/17064.

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Das globale Klimasystem ist ein ausgesprochen komplexes und hochgradig nichtlineares System mit einer Vielzahl von Einflüssen und Interaktionen zwischen Variablen und Parametern. Komplementär zu der Beschreibung des Systems mit globalen Klimamodellen, kann Klima anhand der Interaktionsstruktur des Gesamtsystems durch Netzwerke beschrieben werden. Statt Details so genau wie möglich zu modellieren, werden hier Zeitreihendaten verwendet um zugrundeliegende Strukturen zu finden. Die Herausforderung liegt dann in der Interpretation dieser Strukturen. Um mich der Frage nach der Interpretation von Netzwerkmaßen zu nähern, suche ich nach einem allgemeinen Zusammenhang zwischen Eigenschaften der Netzwerktopologie und Eigenschaften des zugrundeliegenden physikalischen Systems. Dafür werden im Wesentlichen zwei Methoden entwickelt, die auf der Analyse von Temperaturentwicklungen gemäß der Advektions-Diffusions-Gleichung (ADE) basieren. Für die erste Methode wird die ADE mit offenen Randbedingungen und δ-peak Anfangsbedingungen gelöst. Die resultierenden lokalen Temperaturprofile werden verwendet um eine Korrelationsfunktion und damit ein Netzwerk zu definieren. Diese Netzwerke werden analysiert und mit Klimanetzen aus Daten verglichen. Die zweite Methode basiert auf der Diskretisierung der stochastischen ADE. Die resultierende lineare, stochastische Rekursionsgleichung wird verwendet um eine Korrelationsmatrix zu definieren, die nur von der Übergangsmatrix und der Varianz des stochastischen Störungsterms abhängt. Ich konstruiere gewichtete und ungewichtete Netzwerke für vier verschiedene Fälle und schlage Netzwerkmaße vor, die zwischen diesen Systemen zu unterscheiden helfen, wenn nur das Netzwerk und die Knotenpositionen gegeben sind. Die präsentierten Rekonstruktionsmethoden generieren Netzwerke, die konzeptionell und strukturell Klimanetzwerken ähneln und können somit als "proof of concept" der Methode der Klimanetzwerke, sowie als Interpretationshilfe betrachtet werden.
The earth’s climate is an extraordinarily complex, highly non-linear system with a multitude of influences and interactions between a very large number of variables and parameters. Complementary to the description of the system using global climate models, in recent years, a description based on the system’s interaction structure has been developed. Rather than modelling the system in as much detail as possible, here time series data is used to identify underlying large scale structures. The challenge then lies in the interpretation of these structures. In this thesis I approach the question of the interpretation of network measures from a general perspective, in order to derive a correspondence between properties of the network topology and properties of the underlying physical system. To this end I develop two methods of network construction from a velocity field, using the advection-diffusion-equation (ADE) for temperature-dissipation in the system. For the first method, the ADE is solved for δ-peak-shaped initial and open boundary conditions. The resulting local temperature profiles are used to define a correlation function and thereby a network. Those networks are analysed and compared to climate networks from data. Despite the simplicity of the model, it captures some of the most salient features of climate networks. The second network construction method relies on a discretisation of the ADE with a stochastic term. I construct weighted and unweighted networks for four different cases and suggest network measures, that can be used to distinguish between the different systems, based on the topology of the network and the node locations. The reconstruction methods presented in this thesis successfully model many features, found in climate networks from well-understood physical mechanisms. This can be regarded as a justification of the use of climate networks, as well as a tool for their interpretation.
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Dubois, Olivier. "Optimized Schwarz methods for the advection-diffusion equation." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=19701.

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The optimized Schwarz methods were recently introduced to enhance the convergence of the classical Schwarz iteration, by replacing the Dirichlet transmission conditions with different conditions obtained through an optimization of the convergence rate. This is formulated as a min-max problem. These new methods are well-studied for elliptic second order symmetric equations. The purpose of this work is to compute optimized Robin transmission conditions for the advection-diffusion equation in two dimensions, by finding the solution of the min-max problem. The asymptotic expansion, for small mesh size h, of the resulting convergence rate is found: it shows a weak dependence on h, if the overlap is 0(h) or no overlap is used. Numerical experiments illustrate the improved convergence of these optimized methods compared to other Schwarz methods, and also justify the continuous Fourier analysis performed on a simple model problem only. The theoretical asymptotic performance is also verified numerically.
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Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

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Davies, Kevin L. "Declarative modeling of coupled advection and diffusion as applied to fuel cells." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51814.

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The goal of this research is to realize the advantages of declarative modeling for complex physical systems that involve both advection and diffusion to varying degrees in multiple domains. This occurs, for example, in chemical devices such as fuel cells. The declarative or equation-based modeling approach can provide computational advantages and is compatible with physics-based, object-oriented representations. However, there is no generally accepted method of representing coupled advection and diffusion in a declarative modeling framework. This work develops, justifies, and implements a new upstream discretization scheme for mixed advective and diffusive flows that is well-suited for declarative models. The discretization scheme yields a gradual transition from pure diffusion to pure advection without switching events or nonlinear systems of equations. Transport equations are established in a manner that ensures the conservation of material, momentum, and energy at each interface and in each control volume. The approach is multi-dimensional and resolved down to the species level, with conservation equations for each species in each phase. The framework is applicable to solids, liquids, gases, and charged particles. Interactions among species are described as exchange processes which are diffusive if the interaction is inert or advective if it involves chemical reactions or phase change. The equations are implemented in a highly modular and reconfigurable manner using the Modelica language. A wide range of examples are demonstrated—from basic models of electrical conduction and evaporation to a comprehensive model of a proton exchange membrane fuel cell (PEMFC). Several versions of the PEMFC model are simulated under various conditions including polarization tests and a cyclical electrical load. The model is shown to describe processes such as electro-osmotic drag and liquid pore saturation. It can be scaled in complexity from 4000 to 32,000 equations, resulting in a simulation times from 0.2 to 19 s depending on the level of detail. The most complex example is a seven-layer cell with six segments along the length of the channel. The model library is thoroughly documented and made available as a free, open-source software package.
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Dubois, Olivier 1980. "Optimized Schwarz methods for the advection-diffusion equation and for problems with discontinuous coefficients." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103379.

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Optimized Schwarz methods are iterative domain decomposition procedures with greatly improved convergence properties, for solving second order elliptic boundary value problems. The enhanced convergence is obtained by replacing the Dirichlet transmission conditions in the classical Schwarz iteration with more general conditions that are optimized for performance. The convergence is optimized through the solution of a min-max problem. The theoretical study of the min-max problems gives explicit formulas or characterizations for the optimized transmission conditions for practical use, and it permits the analysis of the asymptotic behavior of the convergence.
In the first part of this work, we continue the study of optimized transmission conditions for advection-diffusion problems with smooth coefficients. We derive asymptotic formulas for the optimized parameters for small mesh sizes, in the overlapping and non-overlapping cases, and show that these formulas are accurate when the component of the advection tangential to the interface is not too large.
In a second part, we consider a diffusion problem with a discontinuous coefficient and non-overlapping domain decompositions. We derive several choices of optimized transmission conditions by thoroughly solving the associated min-max problems. We show in particular that the convergence of optimized Schwarz methods improves as the jump in the coefficient increases, if an appropriate scaling of the transmission conditions is used. Moreover, we prove that optimized two-sided Robin conditions lead to mesh-independent convergence. Numerical experiments with two subdomains are presented to verify the analysis. We also report the results of experiments using the decomposition of a rectangle into many vertical strips; some additional analysis is carried out to improve the optimized transmission conditions in that case.
On a third topic, we experiment with different coarse space corrections for the Schwarz method in a simple one-dimensional setting, for both overlapping and non-overlapping subdomains. The goal is to obtain a convergence that does not deteriorate as we increase the number of subdomains. We design a coarse space correction for the Schwarz method with Robin transmission conditions by considering an augmented linear system, which avoids merging the local approximations in overlapping regions. With numerical experiments, we demonstrate that the best Robin conditions are very different for the Schwarz iteration with, and without coarse correction.
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Chakravarty, Lopamudra. "Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-Diffusion Problems." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1523325804305835.

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Fu, Xiaoming. "Reaction-diffusion Equations with Nonlinear and Nonlocal Advection Applied to Cell Co-culture." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0216/document.

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Cette thèse est consacrée à l’étude d’une classe d’équations de réaction-diffusion avec advection non-locale. La motivation vient du mouvement cellulaire avec le phénomène de ségrégation observé dans des expérimentations de co-culture cellulaire. La première partie de la thèse développe principalement le cadre théorique de notre modèle, à savoir le caractère bien posé du problème et le comportement asymptotique des solutions dans les cas d'une ou plusieurs espèces.Dans le Chapitre 1, nous montrons qu'une équation scalaire avec un noyau non-local ayant la forme d'une fonction étagée, peut induire des bifurcations de Turing et de Turing-Hopf avec le nombre d’ondes dominant aussi grand que souhaité. Nous montrons que les propriétés de bifurcation de l'état stable homogène sont intimement liées aux coefficients de Fourier du noyau non-local.Dans le Chapitre 2, nous étudions un modèle d'advection non-local à deux espèces avec inhibition de contact lorsque la viscosité est égale à zéro. En employant la notion de solution intégrée le long des caractéristiques, nous pouvons rigoureusement démontrer le caractère bien posé du problème ainsi que la propriété de ségrégation d'un tel système. Par ailleurs, dans le cadre de la théorie des mesures de Young, nous étudions le comportement asymptotique des solutions. D'un point de vue numérique, nous constatons que sous l'effet de la ségrégation, le modèle d'advection non-locale admet un principe d'exclusion.Dans le dernier Chapitre de la thèse, nous nous intéressons à l'application de nos modèles aux expérimentations de co-culture cellulaire. Pour cela, nous choisissons un modèle hyperbolique de Keller-Segel sur un domaine borné. En utilisant les données expérimentales, nous simulons un processus de croissance cellulaire durant 6 jours dans une boîte de pétri circulaire et nous discutons de l’impact de la propriété de ségrégation et des distributions initiales sur les proportions de la population finale
This thesis is devoted to the study for a class of reaction-diffusion equations with nonlocal advection. The motivation comes from the cell movement with segregation phenomenon observed in cell co-culture experiments. The first part of the thesis mainly develops the theoretical framework of our model, namely the well-posedness and asymptotic behavior of solutions in both single-species and multi-species cases.In Chapter 1, we show a single scalar equation with a step function kernel may display Turing and Turing-Hopf bifurcations with the dominant wavenumber as large as we want. We find the bifurcation properties of the homogeneous steady state is closed related to the Fourier coefficients of the nonlocal kernel.In Chapter 2, we study a two-species nonlocal advection model with contact inhibition when the viscosity equals zero. By employing the notion of the solution integrated along the characteristics, we rigorously prove the well-posedness and segregation property of such a hyperbolic nonlocal advection system. Besides, under the framework of Young measure theory, we investigate the asymptotic behavior of solutions. From a numerical perspective, we find that under the effect of segregation, the nonlocal advection model admits a competitive exclusion principle.In the last Chapter, we are interested in applying our models to a cell co-culturing experiment. To that aim, we choose a hyperbolic Keller-Segel model on a bounded domain. By utilizing the experimental data, we simulate a 6-day process of cell growth in a circular petri dish and discuss the impact of both the segregation property and initial distributions on the finial population proportions
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Martin, Kristin Terese. "Limitations of the Advection-Diffusion Equation for Modeling Tephra Fallout: 1992 Eruption of Cerro Negro Volcano, Nicaragua." [Tampa, Fla.] : University of South Florida, 2004. http://purl.fcla.edu/fcla/etd/SFE0000581.

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Wang, Xiuquan. "Parameter Estimation in the Advection Diffusion Reaction Model With Mean Occupancy Time and Boundary Flux Approaches." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/dissertations/976.

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In this dissertation, we examine an advection diffusion model for insects inhabiting a spatially heterogeneous environment and moving toward a more favorable environment. We first study the effects of adding a term describing drift or advection toward a favorable environment to diffusion models for population dynamics. The diffusion model is a basic linear two-dimensional diffusion equation describing local dispersal of species. The mathematical advection terms are taken to be Fickian and describe directed movement of the population toward the favorable environment. For this model, the landscape is composed of one homogeneous habitat patch embedded in a spatially heterogeneous environment and the boundary of the habitat inhabited by the population acts as a lethal edge. We also derived the mean occupancy time and the boundary flux of the habitat patch. The diffusion rate and advection parameters of the advection diffusion model are estimated based on mean occupancy time and boundary flux. We then introduce two methods for the identification of these coefficients in the model as well as the capture rate. These two new methods have some advantages over other methods of estimating those parameters, including reduced computational cost and ease of use in the field. We further examine the statistical properties of new methods through simulation, and discuss how mean occupancy time and boundary flux could be estimated in field experiments.
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Flegg, Jennifer Anne. "Mathematical modelling of chronic wound healing." Thesis, Queensland University of Technology, 2009. https://eprints.qut.edu.au/40164/1/Jennifer_Flegg_Thesis.pdf.

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Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.
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Books on the topic "Advection-diffusion equation"

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Abarbanel, Saul S. Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Crockett, Stephen Robert. A semi-lagrangian discretization scheme for solving the advection-diffusion equation in two-dimensional simply connected regions. Ottawa: National Library of Canada, 1993.

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Jan, Verwer, ed. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003.

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Hundsdorfer, Willem, and Jan Verwer. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-09017-6.

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1946-, Verwer J. G., ed. Numerical solution of time-dependent advection-diffusion-reaction equations. Berlin: Springer, 2003.

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G, Ostrovskii Alexander, ed. Advection and diffusion in random media: Implications for sea surface temperature anomalies. Dordrecht: Kluwer Academic, 1997.

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Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Adi, Ditkowski, and Langley Research Center, eds. Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Adi, Ditkowski, and Langley Research Center, eds. Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Chuen-Yen, Chow, Chang Sin-Chung, and NASA Glenn Research Center, eds. Application of the space-time conservation element and solution element method to one-dimensional advection-diffusion problems. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 1999.

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Book chapters on the topic "Advection-diffusion equation"

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Clairambault, Jean. "Reaction-Diffusion-Advection Equation." In Encyclopedia of Systems Biology, 1817. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_697.

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Szymkiewicz, Romuald. "Numerical Solution of the Advection-Diffusion Equation." In Numerical Modeling in Open Channel Hydraulics, 263–300. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3674-2_7.

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Povstenko, Yuriy. "Fractional Advection-Diffusion Equation and Associated Diffusive Stresses." In Solid Mechanics and Its Applications, 227–49. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15335-3_9.

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Kajishima, Takeo, and Kunihiko Taira. "Finite-Difference Discretization of the Advection-Diffusion Equation." In Computational Fluid Dynamics, 23–72. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45304-0_2.

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Amattouch, M. R., and H. Belhadj. "An Heuristic Scheme for a Reaction Advection Diffusion Equation." In Heuristics for Optimization and Learning, 223–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58930-1_15.

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Povstenko, Yuriy. "Space-Time-Fractional Advection Diffusion Equation in a Plane." In Lecture Notes in Electrical Engineering, 275–84. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-09900-2_26.

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Lian, Yanping, Gregory J. Wagner, and Wing Kam Liu. "A Meshfree Method for the Fractional Advection-Diffusion Equation." In Meshfree Methods for Partial Differential Equations VIII, 53–66. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51954-8_4.

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Company, R., E. Defez, L. Jódar, and E. Ponsoda. "A Stable CE—SE Numerical Method for Time-Dependent Advection—Diffusion Equation." In Progress in Industrial Mathematics at ECMI 2006, 939–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71992-2_165.

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Buske, D., M. T. Vilhena, C. F. Segatto, and R. S. Quadros. "A General Analytical Solution of the Advection–Diffusion Equation for Fickian Closure." In Integral Methods in Science and Engineering, 25–34. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8238-5_4.

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Skiba, Yuri N., and Roberto Carlos Cruz-Rodríguez. "Application of Splitting Algorithm for Solving Advection-Diffusion Equation on a Sphere." In Progress in Industrial Mathematics at ECMI 2018, 285–90. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27550-1_35.

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Conference papers on the topic "Advection-diffusion equation"

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Marinho, Gisele Moraes, Jader Lugon Júnior, Diego Campos Knupp, Antônio J. Silva Neto, Antônio J. Silva Neto, and Joao Flávio Vieira Vasconcellos. "Inverse Problem in Space Fractional Advection Diffusion Equation." In CNMAC 2019 - XXXIX Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2020. http://dx.doi.org/10.5540/03.2020.007.01.0394.

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Laouar, Zineb, and Nouria Arar. "Legendre-Galerkin approximation for the advection-diffusion equation." In 10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0116292.

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Amali, Onjefu, and Nwojo N. Agwu. "Finite element method for solving the advection-diffusion equation." In 2017 13th International Conference on Electronics, Computer and Computation (ICECCO). IEEE, 2017. http://dx.doi.org/10.1109/icecco.2017.8333328.

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Dhawan, S., S. Rawat, S. Kumar, and S. Kapoor. "Solution of advection diffusion equation using finite element method." In 2011 Fourth International Conference on Modeling, Simulation and Applied Optimization (ICMSAO). IEEE, 2011. http://dx.doi.org/10.1109/icmsao.2011.5775634.

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Merzari, Elia, W. David Pointer, and Paul Fischer. "A POD-Based Solver for the Advection-Diffusion Equation." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-01022.

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Abstract:
We present a methodology based on proper orthogonal decomposition (POD). We have implemented the POD-based solver in the large eddy simulation code Nek5000 and used it to solve the advection-diffusion equation for temperature in cases where buoyancy is not present. POD allows for the identification of the most energetic modes of turbulence when applied to a sufficient set of snapshots generated through Nek5000. The Navier-Stokes equations are then reduced to a set of ordinary differential equations by Galerkin projection. The flow field is reconstructed and used to advect the temperature on longer time scales and potentially coarser grids. The methodology is validated and tested on two problems: two-dimensional flow past a cylinder and three-dimensional flow in T-junctions. For the latter case, the benchmark chosen corresponds to the experiments of Hirota et al., who performed particle image velocimetry on the flow in a counterflow T-junction. In both test problems the dynamics of the reduced-order model reproduce well the history of the projected modes when a sufficient number of equations are considered. The dynamics of flow evolution and the interaction of different modes are also studied in detail for the T-junction.
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Jannelli, Alessandra, Marianna Ruggieri, and Maria Paola Speciale. "Analytical and numerical solutions of fractional type advection-diffusion equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992675.

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Popov, V., S. Ahmed, and M. Idris Qureshi. "Simulation of constructed wetland performance using the advection diffusion equation." In WASTE MANAGEMENT 2008. Southampton, UK: WIT Press, 2008. http://dx.doi.org/10.2495/wm080381.

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Chen, P., G. Tao, and M. Dong. "Analytical Solution for Unidirectional Advection-diffusion Equation with Variable Viscosities." In 74th EAGE Conference and Exhibition incorporating EUROPEC 2012. Netherlands: EAGE Publications BV, 2012. http://dx.doi.org/10.3997/2214-4609.20148656.

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Leal Toledo, R. C., V. Ruas, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A Mixed Least-Squares Formulation for the Transient Advection-Diffusion Equation." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498562.

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Stinguel, L., and R. Guirardello. "Numerical resolution of the advection-diffusion equation with non-linear adsorption isotherm." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044109.

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Reports on the topic "Advection-diffusion equation"

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CHRISTON, MARK A., THOMAS E. VOTH, and MARIO J. MARTINEZ. Generalized Fourier Analyses of Semi-Discretizations of the Advection-Diffusion Equation. Office of Scientific and Technical Information (OSTI), November 2002. http://dx.doi.org/10.2172/805879.

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Hughes, Thomas J., and Garth N. Wells. Conservation Properties for the Galerkin and Stabilised Forms of the Advection-Diffusion and Incompressible Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2005. http://dx.doi.org/10.21236/ada438123.

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Carasso, Alfred S. Data assimilation in 2D nonlinear advection diffusion equations, using an explicit stabilized leapfrog scheme run backward in time. Gaithersburg, MD: National Institute of Standards and Technology, 2022. http://dx.doi.org/10.6028/nist.tn.2227.

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