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Academic literature on the topic 'Reaction-convection-diffusion equations'

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Published: 14 March 2023

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Journal articles on the topic "Reaction-convection-diffusion equations"

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El-Wakil, S. A., A. Elhanbaly, and M. A. Abdou. "On the Diffusion-Convection-Reaction Equations." Physica Scripta 60, no. 3 (September 1, 1999): 207–10. http://dx.doi.org/10.1238/physica.regular.060a00207.

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de Pablo, Arturo, and Ariel Sánchez. "Global Travelling Waves in Reaction–Convection–Diffusion Equations." Journal of Differential Equations 165, no. 2 (August 2000): 377–413. http://dx.doi.org/10.1006/jdeq.2000.3781.

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Iliescu, Traian, and Zhu Wang. "Variational multiscale proper orthogonal decomposition: Convection-dominated convection-diffusion-reaction equations." Mathematics of Computation 82, no. 283 (March 18, 2013): 1357–78. http://dx.doi.org/10.1090/s0025-5718-2013-02683-x.

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Giere, Swetlana, Traian Iliescu, Volker John, and David Wells. "SUPG reduced order models for convection-dominated convection–diffusion–reaction equations." Computer Methods in Applied Mechanics and Engineering 289 (June 2015): 454–74. http://dx.doi.org/10.1016/j.cma.2015.01.020.

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Choudhury, A. H. "Wavelet Method for Numerical Solution of Parabolic Equations." Journal of Computational Engineering 2014 (February 27, 2014): 1–12. http://dx.doi.org/10.1155/2014/346731.

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We derive a highly accurate numerical method for the solution of parabolic partial differential equations in one space dimension using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method using some special types of basis functions obtained by integrating Daubechies functions which are compactly supported and differentiable. The time variable is discretized by using various classical finite difference schemes. Theoretical and numerical results are obtained for problems of diffusion, diffusion-reaction, convection-diffusion, and convection-diffusion-reaction with Dirichlet, mixed, and Neumann boundary conditions. The computed solutions are highly favourable as compared to the exact solutions.
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Phongthanapanich, Sutthisak, and Pramote Dechaumphai. "A CHARACTERISTIC-BASED FINITE VOLUME ELEMENT METHOD FOR CONVECTION-DIFFUSION-REACTION EQUATION." Transactions of the Canadian Society for Mechanical Engineering 32, no. 3-4 (September 2008): 549–60. http://dx.doi.org/10.1139/tcsme-2008-0037.

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A two-dimensional convection-diffusion-reaction equation is discretized by the finite volume element method on triangular meshes. Time-dependent convection-diffusion-reaction equation is developed along the characteristic path using the characteristic-based scheme, while the finite volume method is employed for deriving the discretized equations. The concept of the finite element technique is applied to estimate the gradient quantities at the cell faces of the finite volume. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. The robustness and the accuracy of the method have been evaluated by using available analytical and numerical solutions of the pure-convection, convection-diffusion and convection-diffusion-reaction problems.
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Lu, Yunguang, and Willi Jäger. "On Solutions to Nonlinear Reaction–Diffusion–Convection Equations with Degenerate Diffusion." Journal of Differential Equations 170, no. 1 (February 2001): 1–21. http://dx.doi.org/10.1006/jdeq.2000.3800.

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Ei, Shin-Ichiro. "The effect of nonlocal convection on reaction-diffusion equations." Hiroshima Mathematical Journal 17, no. 2 (1987): 281–307. http://dx.doi.org/10.32917/hmj/1206130067.

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Geiser, Jürgen, Jose L. Hueso, and Eulalia Martínez. "Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations." Mathematics 8, no. 3 (February 25, 2020): 302. http://dx.doi.org/10.3390/math8030302.

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This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection–diffusion–reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers’ and Maxwell–Stefan diffusion equations.
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Sarrico, C. O. R. "New singular travelling waves for convection–diffusion–reaction equations." Journal of Physics A: Mathematical and Theoretical 53, no. 15 (March 26, 2020): 155202. http://dx.doi.org/10.1088/1751-8121/ab7c1d.

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Dissertations / Theses on the topic "Reaction-convection-diffusion equations"

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Sun, Xiaodi. "Metastable dynamics of convection-diffusion-reaction equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34630.pdf.

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Seymen, Zahire. "Solving Optimal Control Time-dependent Diffusion-convection-reaction Equations By Space Time Discretizations." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615399/index.pdf.

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Optimal control problems (OCPs) governed by convection dominated diffusion-convection-reaction equations arise in many science and engineering applications such as shape optimization of the technological devices, identification of parameters in environmental processes and flow control problems. A characteristic feature of convection dominated optimization problems is the presence of sharp layers. In this case, the Galerkin finite element method performs poorly and leads to oscillatory solutions. Hence, these problems require stabilization techniques to resolve boundary and interior layers accurately. The Streamline Upwind Petrov-Galerkin (SUPG) method is one of the most popular stabilization technique for solving convection dominated OCPs. The focus of this thesis is the application and analysis of the SUPG method for distributed and boundary OCPs governed by evolutionary diffusion-convection-reaction equations. There are two approaches for solving these problems: optimize-then-discretize and discretize-then-optimize. For the optimize-then-discretize method, the time-dependent OCPs is transformed to a biharmonic equation, where space and time are treated equally. The resulting optimality system is solved by the finite element package COMSOL. For the discretize-then-optimize approach, we have used the so called allv at-once method, where the fully discrete optimality system is solved as a saddle point problem at once for all time steps. A priori error bounds are derived for the state, adjoint, and controls by applying linear finite element discretization with SUPG method in space and using backward Euler, Crank- Nicolson and semi-implicit methods in time. The stabilization parameter is chosen for the convection dominated problem so that the error bounds are balanced to obtain L2 error estimates. Numerical examples with and without control constraints for distributed and boundary control problems confirm the effectiveness of both approaches and confirm a priori error estimates for the discretize-then-optimize approach.
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Hernandez, Velazquez Hector Alonso. "Numerical stabilization for multidimensional coupled convection-diffusion-reaction equations: Applications to continuum dislocation transport." Doctoral thesis, Universite Libre de Bruxelles, 2017. https://dipot.ulb.ac.be/dspace/bitstream/2013/257833/6/contratHH.pdf.

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Partial differential equations having diffusive, convective and reactive terms appear naturally in the modeling of a large variety of processes of practical interest in several branches of science such as biology, chemistry, economics, physics, physiology and materials science. Moreover, in some instances several species or components interact with each other requiring to solve strongly coupled systems of convection-diffusion-reaction equations. Of special interest for us is the numerical treatment of the advection dominated continuum dislocation transport equations used to describe the plastic behavior of crystalline materials.Analytical solutions for such equations are extremely scarce and practically limited to linear equations with homogeneous coefficients and simple initial and boundary conditions. Therefore, resorting to numerical approximations is the most affordable and often the only viable strategy to deal with such models. However, when classical numerical methods are used to approximate the solutions of such equations, even in the simplest one dimensional case in the steady state regime for a single equation, instabilities in the form of node to node spurious oscillations are found when the convective or reactive terms dominate over the diffusive term.To address such issues, stabilization techniques have been developed over the years in order to handle such transport equations by numerical means, overcoming the stability difficulties. However, such stabilization techniques are most often suited for particular problems. For instance the Streamline Upwind Petrov-Galerkin method, to name only one of the most well-known, successfully eliminates spurious oscillations for single advection-diffusion equations when its advective form is discretized, but have been shown useless if the divergence form is used instead. Additionally, no extensive work has been carried out for systems of coupled equations. The reason for this immaturity is the lack of a maximum principle when going from a single transport equation towards systems of coupled equations.The main aim of this work is to present a stabilization technique for systems of coupled multidimensional convection-diffusion-reaction equations based on coefficient perturbations. These perturbations are optimally chosen in such a way that certain compatibility conditions analogous to a maximum principle are satisfied. Once the computed perturbations are injected in the classical Bubnov-Galerkin finite element method, they provide smooth and stable numerical approximations.Such a stabilization technique is first developed for the single one-dimensional convection-diffusion-reaction equation. Rigorous proof of its effectiveness in rendering unconditionally stable numerical approximations with respect to the space discretization is provided for the convection-diffusion case via the fulfillment of the discrete maximum principle. It is also demonstrated and confirmed by numerical assessments that the stabilized solution is consistent with the discretized partial differential equation, since it converges to the classical Bubnov-Galerkin solution if the mesh Peclet number is small enough. The corresponding proofs for the diffusion-reaction and the general convection-diffusion-reaction cases can be obtained in a similar manner. Furthermore, it is demonstrated that this stabilization technique is applicable irrespective of whether the advective or the divergence form is used for the spatial discretization, making it highly flexible and general. Subsequently the stabilization technique is extended to the one-dimensional multiple equations case by using the superposition principle, a well-known strategy used when solving non-homogeneous second order ordinary differential equations. Finally, the stabilization technique is applied to mutually perpendicular spatial dimensions in order to deal with multidimensional problems.Applications to several prototypical linear coupled systems of partial differential equations, of interest in several scientific disciplines, are presented. Subsequently the stabilization technique is applied to the continuum dislocation transport equations, involving their non-linearity, their strongly coupled character and the special boundary conditions used in this context; a combination of additional difficulties which most traditional stabilization techniques are unable to deal with. The proposed stabilization scheme has been successfully applied to these equations. Its effectiveness in stabilizing the classical Bubnov-Galerkin scheme and being consistent with the discretized partial differential equation are both demonstrated in the numerical simulations performed. Such effectiveness remains unaffected when different types of dislocation transport models with constant or variable length scales are used.These results allow envisioning the use of the developed technique for simulating systems of strongly coupled convection-diffusion-reaction equations with an affordable computational effort. In particular, the above mentioned crystal plasticity models can now be handled with reasonable computation times without the use of extraordinary computational power, but still being able to render accurate and physically meaningful numerical approximations.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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Ahmed, Naveed, and Gunar Matthies. "Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations." Cambridge University Press, 2015. https://tud.qucosa.de/id/qucosa%3A39044.

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We present the analysis for the higher order continuous Galerkin−Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin−Petrov and discontinuous Galerkin time discretization schemes will be given.
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Mbroh, Nana Adjoah. "On the method of lines for singularly perturbed partial differential equations." University of the Western Cape, 2017. http://hdl.handle.net/11394/5679.

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Magister Scientiae - MSc
Many chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to recourse to numerical approaches to determine suitable approximations to the solution of such equations. For solutions possessing sharp spatial transitions (such as boundary or interior layers), standard numerical methods have shown limitations as they fail to capture large gradients. The method of lines (MOL) is one of the numerical methods used to solve PDEs. It proceeds by the discretization of all but one dimension leading to systems of ordinary di erential equations. In the case of time-dependent PDEs, the MOL consists of discretizing the spatial derivatives only leaving the time variable continuous. The process results in a system to which a numerical method for initial value problems can be applied. In this project we consider various types of singularly perturbed time-dependent PDEs. For each type, using the MOL, the spatial dimensions will be discretized in many different ways following fitted numerical approaches. Each discretisation will be analysed for stability and convergence. Extensive experiments will be conducted to confirm the analyses.
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Ahmed, Naveed [Verfasser], and Lutz [Akademischer Betreuer] Tobiska. "Stabilized finite element methods applied to transient convection-diffusion-reaction and population balance equations / Naveed Ahmed. Betreuer: Lutz Tobiska." Magdeburg : Universitätsbibliothek, 2011. http://d-nb.info/1047559021/34.

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Simon, Kristin [Verfasser]. "Higher order stabilized surface finite element methods for diffusion-convection-reaction equations on surfaces with and without boundary / Kristin Simon." Magdeburg : Universitätsbibliothek, 2017. http://d-nb.info/1147834520/34.

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Lao, Kun Leng. "Multigrid algorithm based on cyclic reduction for convection diffusion equations." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148274.

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Nadukandi, Prashanth. "Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/109155.

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We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi: 10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045- 7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi: 10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small.
Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion
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Galbally, David. "Nonlinear model reduction for uncertainty quantification in large-scale inverse problems : application to nonlinear convection-diffusion-reaction equation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43079.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.
Includes bibliographical references (p. 147-152).
There are multiple instances in science and engineering where quantities of interest are evaluated by solving one or several nonlinear partial differential equations (PDEs) that are parametrized in terms of a set of inputs. Even though well-established numerical techniques exist for solving these problems, their computational cost often precludes their use in cases where the outputs of interest must be evaluated repeatedly for different values of the input parameters such as probabilistic analysis applications. In this thesis we present a model reduction methodology that combines efficient representation of the nonlinearities in the governing PDE with an efficient model-constrained, greedy algorithm for sampling the input parameter space. The nonlinearities in the PDE are represented using a coefficient-function approximation that enables the development of an efficient offline-online computational procedure where the online computational cost is independent of the size of the original high-fidelity model. The input space sampling algorithm used for generating the reduced space basis adaptively improves the quality of the reduced order approximation by solving a PDE-constrained continuous optimization problem that targets the output error between the reduced and full order models in order to determine the optimal sampling point at every greedy cycle. The resulting model reduction methodology is applied to a highly nonlinear combustion problem governed by a convection-diffusion-reaction PDE with up to 3 input parameters. The reduced basis approximation developed for this problem is up to 50, 000 times faster to solve than the original high-fidelity finite element model with an average relative error in prediction of outputs of interest of 2.5 - 10-6 over the input parameter space. The reduced order model developed in this thesis is used in a novel probabilistic methodology for solving inverse problems.
(cont) The extreme computational cost of the Bayesian framework approach for inferring the values of the inputs that generated a given set of empirically measured outputs often precludes its use in practical applications. In this thesis we show that using a reduced order model for running the Markov
by David Galbally.
S.M.
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Books on the topic "Reaction-convection-diffusion equations"

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Gilding, Brian H. Travelling Waves in Nonlinear Diffusion-Convection Reaction. Basel: Birkhäuser Basel, 2004.

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H, Carpenter Mark, and Langley Research Center, eds. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2001.

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H, Carpenter Mark, and Langley Research Center, eds. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2001.

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H, Carpenter Mark, and Langley Research Center, eds. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2001.

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C, Sorensen D., and Institute for Computer Applications in Science and Engineering., eds. An asymptotic induced numerical method for the convection-diffusion-reaction equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1988.

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Layer-adapted meshes for reaction-convection-diffusion problems. Heidelberg: Springer, 2010.

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Elementary feedback stabilization of the linear reaction-convection-diffusion equation and the wave equation. Heidelberg: Springer, 2010.

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Liu, Weijiu. Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04613-1.

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Codina, R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Barcelona, Spain: International Center for Numerical Methods in Engineering, 1996.

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A, Monaco Lisa, and United States. National Aeronautics and Space Administration., eds. Convective flow effects on protein crystal growth: First semi-annual progress report, NASA grant NAG8-950, period of performance 2/1/93 through 7/31/93. Huntsville, Ala: Center for Microgravity and Materials Research, University of Alabama in Huntsville, 1993.

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Book chapters on the topic "Reaction-convection-diffusion equations"

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Volpert, Vitaly. "Reaction-diffusion Problems with Convection." In Elliptic Partial Differential Equations, 391–451. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0813-2_6.

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Cherniha, Roman, Mykola Serov, and Oleksii Pliukhin. "Introduction." In Nonlinear Reaction-Diffusion-Convection Equations, 1–17. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315154848-1.

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Cherniha, Roman, Mykola Serov, and Oleksii Pliukhin. "Lie symmetries of reaction‐diffusion‐convection equations." In Nonlinear Reaction-Diffusion-Convection Equations, 19–75. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315154848-2.

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Cherniha, Roman, Mykola Serov, and Oleksii Pliukhin. "Conditional symmetries of reaction-diffusion-convection equations." In Nonlinear Reaction-Diffusion-Convection Equations, 77–133. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315154848-3.

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Cherniha, Roman, Mykola Serov, and Oleksii Pliukhin. "Exact solutions of reaction-diffusion-convection equations and their applications." In Nonlinear Reaction-Diffusion-Convection Equations, 135–90. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315154848-4.

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Cherniha, Roman, Mykola Serov, and Oleksii Pliukhin. "The method of additional generating conditions for constructing exact solutions." In Nonlinear Reaction-Diffusion-Convection Equations, 191–218. Boca Raton, Florida : CRC Press, [2018]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315154848-5.

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Howes, F. A. "Multi-dimensional reaction-convection-diffusion equations." In Ordinary and Partial Differential Equations, 217–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074730.

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Gilding, Brian H., and Robert Kersner. "Power-law equations." In Travelling Waves in Nonlinear Diffusion-Convection Reaction, 59–67. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7964-4_7.

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Gilding, Brian H., and Robert Kersner. "Wavefronts and unbounded waves for power-law equations." In Travelling Waves in Nonlinear Diffusion-Convection Reaction, 139–55. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7964-4_12.

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Barrenechea, G. R., V. John, and P. Knobloch. "A Nonlinear Local Projection Stabilization for Convection-Diffusion-Reaction Equations." In Numerical Mathematics and Advanced Applications 2011, 237–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33134-3_26.

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Conference papers on the topic "Reaction-convection-diffusion equations"

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Rocha, E. M., M. M. Rodrigues, Alberto Cabada, Eduardo Liz, and Juan J. Nieto. "Exact and Approximate Solutions of Reaction-Diffusion-Convection Equations." In MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE: International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine. AIP, 2009. http://dx.doi.org/10.1063/1.3142946.

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Schecter, Stephen, Dan Marchesin, Lucas Furtado, and Grigori Chapiro. "Stability of interacting traveling waves in reaction-convection-diffusion systems." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0258.

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Ghosh, Anirban, Jung-Hee Seo, and Rajat Mittal. "Coupled Fluid-Chemical Computational Modeling of Anticoagulation Therapies in a Stented Artery." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52638.

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Stent thrombosis is a major complication that occurs after the placement of stents in the coronary artery through balloon angioplasty. The common treatment for stent thrombosis is to provide patients with anticoagulant and antiplatelet therapy through the bloodstream. This study uses numerical modeling to compare two delivery methods of heparin anticoagulant to the arterial wall to reduce thrombus formation: through the flow and via a drug-eluting stent. A unique computational fluid dynamics model is developed that couples an incompressible flow solver with a convection-diffusion-reaction equation solver. The flow solver uses a sharp-interface immersed boundary method on a Cartesian grid to characterize pulsatile flow over the curved wires of the stent. Concurrently, the convection-diffusion-reaction equations are solved for the 19 coupled reactions that make up the coagulation cascade and heparin interactions, as well as reaction and transport equations for both active and inactive platelet species. The simulation is run with input boundary conditions of steady flow, pulsatile Poiseuille flow, and a Womersley flow profile. Results are collected for the bare metal stent case, anticoagulant delivered through the bloodstream, and anticoagulant delivered through a drug-eluting stent. The results generally find that the drug-eluting stent delivery of anticoagulant is more effective in reducing platelet activation and clotting, while also providing a more localized anticoagulant distribution.
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Edwards, Maegan, John P. Kizito, and Rodward L. Hewlin. "A Time-Dependent Two Species Explicit Finite Difference Computational Model for Analyzing Diffusion in a Drug Eluting Stented Coronary Artery Wall: a Phase I Study." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-95803.

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Abstract This paper outlines results for a mathematical drug transport model developed for simulating the transport of a hydrophobic drug in a drug eluting stented coronary arterial vessel wall. The mathematical drug transport model incorporates the diffusion equation with a two species (free and bound drug) reversible equilibrium reaction source term to account for tissue binding. The model is solved by an explicit 2-D finite difference method for discretizing and solving the free and bound convection equations with anisotropic vascular drug diffusivities. The relative reaction rates control the interconversion of drug between the free and bound states. Results include provide a glance at the relative distribution of the two drug forms in a two-dimensional model of the arterial vessel wall. The model also reveals how a single species drug delivery model cannot accurately predict the distribution of bound drug.
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Kamel, John K., and Samuel Paolucci. "Numerical Simulation of a Chemical Vapor Deposition/Infiltration Reactor." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16039.

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A chemical vapor deposition/infiltration reactor used to manufacture carbon aircraft brakes has been simulated numerically. This simulation accounts for a homogeneous gas reaction mechanism as well as a heterogeneous surface reaction mechanism. Non-Boussinesq equations are used to predict fluid flow, heat transfer, and species concentrations inside the reactor and porous brakes. A time-splitting algorithm is used to overcome stiffness associated with the reactions. A commercial code is used to solve for the convection/diffusion step while an implicit time-integration algorithm is used to solve for the reaction step. Results showing the flow, temperature and concentration fields, as well as the deposition rate of carbon, are presented.
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Gherman, Bogdan, Florin Gabriel Florean, Cristian Cârlănescu, and Ionuţ Porumbel. "On the Influence of the Combustion Model on the Result of Turbulent Flames Numerical Simulations." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-69255.

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The paper is aimed at evaluating the impact of the combustion model on the accuracy of the results of the numerical simulations of turbulent reactive flows. For this, two numerical simulations of the well known Sandia Flame D case are carried out: a three-dimensional RANS integration of the Navier–Stokes equations using the Eddy Dissipation combustion Model (EDM), and a one-dimensional one, where simplified reaction–diffusion equations are numerically integrated over the radial direction, while the axial convection is modeled by empirical laws. The one-dimensional simulation, however, is based on a more physics related combustion model, the Linear Eddy Mixing model, which also controls the radial turbulent mixing and the large scale radial convection. The results of the two numerical simulations are compared to experimental data in the literature, showing a significantly better accuracy of the Linear Eddy Mixing (LEM) numerical simulation.
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Huang, Wei, and Wilson K. S. Chiu. "Heat and Mass Transfer in a CVD Optical Fiber Coating Process." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56320.

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In this paper, we study the chemical vapor deposition (CVD) process used to hermetically coat optical fibers during draw. Temperature is calculated by coupling radiation and convection heat transfer by the reactor walls and gas flow with a radially-lumped heat transfer model for the moving optical fiber. Multi-component species diffusion is modeled using the Maxwell-Stefan equations. Gas-phase reaction kinetics is modeled using a 2-step chemical kinetics mechanism derived from RRKM theory with detailed kinetics data compiled from literature. Surface reaction kinetics are described using collision theory in which a sticking coefficient is used as an empirical parameter to predict surface reactions. A parameter study is carried out with various optical fiber inlet temperature and drawing speed, and validated with experiment results.
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Tourlomousis, Filippos, and Robert C. Chang. "Computational Modeling of 3D Printed Tissue-on-a-Chip Microfluidic Devices as Drug Screening Platforms." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38454.

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Physiological tissue-on-a-chip technology is enabled by adapting microfluidics to create micro scale drug screening platforms that replicate the complex drug transport and reaction processes in the human liver. The ability to incorporate three-dimensional (3d) tissue models using layered fabrication approaches into devices that can be perfused with drugs offer an optimal analog of the in vivo scenario. The dynamic nature of such in vitro metabolism models demands reliable numerical tools to determine the optimum tissue fabrication process, flow, material, and geometric parameters for the most effective metabolic conversion of the perfused drug into the liver microenvironment. Thus, in this modeling-based study, the authors focus on modeling of in vitro 3d microfluidic microanalytical microorgan devices (3MD), where the human liver analog is replicated by 3d cell encapsulated alginate hydrogel based tissue-engineered constructs. These biopolymer constructs are hosted in the chamber of the 3MD device serving as walls of the microfluidic array of channels through which a fluorescent drug substrate is perfused into the microfluidic printed channel walls at a specified volumetric flow rate assuring Stokes flow conditions (Re<<1). Due to the porous nature of the hydrogel walls, a metabolized drug product is collected as an effluent stream at the outlet port. A rigorous modeling approached aimed to capture both the macro and micro scale transport phenomena is presented. Initially, the Stokes Flow Equations (free flow regime) are solved in combination with the Brinkman Equations (porous flow regime) for the laminar velocity profile and wall shear stresses in the whole shear mediated flow regime. These equations are then coupled with the Convection-Diffusion Equation to yield the drug concentration profile by incorporating a reaction term described by the Michael-Menten Kinetics model. This effectively yields a convection-diffusion–cell kinetics model (steady state and transient), where for the prescribed process and material parameters, the drug concentration profile throughout the flow channels can be predicted. A key consideration that is addressed in this paper is the effect of cell mechanotransduction, where shear stresses imposed on the encapsulated cells alter the functional ability of the liver cell enzymes to metabolize the drug. Different cases are presented, where cells are incorporated into the geometric model either as voids that experience wall shear stress (WSS) around their membrane boundaries or as solid materials, with linear elastic properties. As a last step, transient simulations are implemented showing that there exists a tradeoff with respect the drug metabolized effluent product between the shear stresses required and the residence time needed for drug diffusion.
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Baier, Tobias, Swaty Mohanty, Klaus Stefan Drese, Federica Rampf, Jungtae Kim, and Friedhelm Scho¨nfeld. "Modelling Immunomagnetic Cell Capture in CFD." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62176.

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The separation of cells from a complex sample by immunomagnetic capture has become a standard technique in the last decade and has also obtained increased attention for microfluidic applications. We present a model that incorporates binding kinetics for the formation of cell-bead complexes, which can easily be integrated into a computational fluid dynamics (CFD) code. The model relies on the three equation types: Navier-Stokes equations governing the fluid dynamics, convection-diffusion equations for non-magnetic cells and a Nernst-Planck type equation governing the temporal evolution of cell-bead complex concentrations. The latter two equations are augmented by appropriate ‘reaction’ terms governing the binding kinetics which is formulated as a population rate balance between creation and annihilation of cell-bead complexes. First, the simulation results show, that by means of the developed approach appropriate parameter sets can be identified which allow for a continuous separation of tagged cells (cell/bead complexes) from non-magnetic particles such as non-target cells entering with the target cells. Moreover tagged cells can be, to a certain extend, separated from unbound beads. Second, the computed concentrations at the outlet show a drastic drop for higher cell/bead complexes beyond a certain number of beads per cell. We show that a critical number of beads per cells exists where the binding is considerably reduced or the reaction cascade ceases completely. This occurs when cell/bead complex have a similar magnetic mobility as the free magnetic beads. The presented CFD model has been applied to the simulation of a generic continuous cell separation system showing that the method facilitates the design of magnetophoretic systems.
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Serra, Christophe, Nicolas Sary, and Guy Schlatter. "Numerical Simulations of Macromolecular Syntheses in Micro-Mixers: Towards a Better Control of the Polymerization." In ASME 3rd International Conference on Microchannels and Minichannels. ASMEDC, 2005. http://dx.doi.org/10.1115/icmm2005-75044.

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This paper investigates the modeling of styrene free radical polymerization in two different types of micro-mixer for which the wall temperature is kept constant. The simulations are performed with the help of the finite elements method which allows solving simultaneously partial differential equations resulting from the hydrodynamics, thermal and mass transfer (convection, diffusion and chemical reaction). The different micro-mixers modeled are on one hand an interdigital multilamination micro-mixer with a large focusing section and on the other hand a simple T-junction with three different radii followed by a tube reactor having the same radius. The results are expressed in terms of reactor temperature, polydispersity index, number-average degree of polymerization and monomer conversion for different values of the chemical species diffusion coefficient. Despite of the heat released by the polymerization reaction, it was found that the thermal transfer in such microfluidic devices is high enough to ensure isothermal conditions. Concerning the polydispersity index, the range of diffusion coefficients over which the polydispersity index can be maintained close to the theoretical value for ideal conditions increases as the tube reactor radius decreases. The interdigital multilamination micro-mixer was found to act as a T-junction and tube reactor of 0,72 mm ID but gives up to 15% higher monomer conversion. This underlines that the use of microfluidic devices can lead to a better control of the polymerization.
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Reports on the topic "Reaction-convection-diffusion equations"

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Manzini, Gianmarco, Andrea Cangiani, and Oliver Sutton. The Conforming Virtual Element Method for the convection-diffusion-reaction equation with variable coeffcients. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1159207.

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Manzini, Gianmarco, Andrea Cangiani, and Oliver Sutton. Numerical results using the conforming VEM for the convection-diffusion-reaction equation with variable coefficients. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1159206.

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