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Author: Sanjay Komala Sheshachala
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Nonlinear reaction-convection-diffusion equations are encountered in modeling of a variety of natural phenomena such as in chemical reactions, population dynamics and contaminant dispersal. When the scale of convective and reactive phenomena are large, Galerkin finite element solution fails. As a remedy, Orthogonal Subgrid Scale stabilization is applied to the finite element formulation. It has its origins in the Variational Multi Scale approach. It is based on a fine grid - coarse grid component sum decomposition of solution and utilizes the fine grid solution orthogonal to the residual of the finite element coarse grid solution as a correction term. With selective mesh refinement, a stabilized oscillation-free solution that can capture sharp layers is obtained. Newton Raphson method is utilized for the linearization of nonlinear reaction terms. Backward difference scheme is used for time integration. The formulation is tested for cases with standalone and coupled systems of transient nonlinear reaction-convection-diffusion equations. Method of manufactured solution is used to test for correctness and bug-free implementation of the formulation. In the error analysis, optimal convergence is achieved. Applications in channel flow, cavity flow and predator-prey model is used to highlight the need and effectiveness of the stabilization technique.
Author: Sanjay Komala Sheshachala
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Nonlinear reaction-convection-diffusion equations are encountered in modeling of a variety of natural phenomena such as in chemical reactions, population dynamics and contaminant dispersal. When the scale of convective and reactive phenomena are large, Galerkin finite element solution fails. As a remedy, Orthogonal Subgrid Scale stabilization is applied to the finite element formulation. It has its origins in the Variational Multi Scale approach. It is based on a fine grid - coarse grid component sum decomposition of solution and utilizes the fine grid solution orthogonal to the residual of the finite element coarse grid solution as a correction term. With selective mesh refinement, a stabilized oscillation-free solution that can capture sharp layers is obtained. Newton Raphson method is utilized for the linearization of nonlinear reaction terms. Backward difference scheme is used for time integration. The formulation is tested for cases with standalone and coupled systems of transient nonlinear reaction-convection-diffusion equations. Method of manufactured solution is used to test for correctness and bug-free implementation of the formulation. In the error analysis, optimal convergence is achieved. Applications in channel flow, cavity flow and predator-prey model is used to highlight the need and effectiveness of the stabilization technique.
Author: Christopher Alan Kennedy
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 56
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Book Description
Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N=2, additive Runge-Kutta ARK methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK methods have vanishing stability functions for very large values of the stiff scaled eigenvalue and retain high stability efficiency in the absence of stiffness.
Author: Guy P. Brasseur
Publisher: Cambridge University Press
ISBN: 1108210953
Category : Science
Languages : en
Pages : 631
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Book Description
Mathematical modeling of atmospheric composition is a formidable scientific and computational challenge. This comprehensive presentation of the modeling methods used in atmospheric chemistry focuses on both theory and practice, from the fundamental principles behind models, through to their applications in interpreting observations. An encyclopaedic coverage of methods used in atmospheric modeling, including their advantages and disadvantages, makes this a one-stop resource with a large scope. Particular emphasis is given to the mathematical formulation of chemical, radiative, and aerosol processes; advection and turbulent transport; emission and deposition processes; as well as major chapters on model evaluation and inverse modeling. The modeling of atmospheric chemistry is an intrinsically interdisciplinary endeavour, bringing together meteorology, radiative transfer, physical chemistry and biogeochemistry, making the book of value to a broad readership. Introductory chapters and a review of the relevant mathematics make this book instantly accessible to graduate students and researchers in the atmospheric sciences.
Author: Albert Cohen
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
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Book Description
Author: Timon Rabczuk
Publisher: Springer Nature
ISBN: 3031366441
Category : Technology & Engineering
Languages : en
Pages : 456
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Book Description
Machine learning (ML) approaches have been extensively and successfully employed in various areas, like in economics, medical predictions, face recognition, credit card fraud detection, and spam filtering. There is clearly also the potential that ML techniques developed in Engineering and the Sciences will drastically increase the possibilities of analysis and accelerate the design to analysis time. With the use of ML techniques, coupled to conventional methods like finite element and digital twin technologies, new avenues of modeling and simulation can be opened but the potential of these ML techniques needs to still be fully harvested, with the methods developed and enhanced. The objective of this book is to provide an overview of ML in Engineering and the Sciences presenting fundamental theoretical ingredients with a focus on the next generation of computer modeling in Engineering and the Sciences in which the exciting aspects of machine learning are incorporated. The book is of value to any researcher and practitioner interested in research or applications of ML in the areas of scientific modeling and computer aided engineering.
Author: Carmelo Clavero
Publisher: Springer Science & Business Media
ISBN: 3642196659
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.
Author: Osvaldo Gervasi
Publisher: Springer
ISBN: 3319951653
Category : Computers
Languages : en
Pages : 804
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Book Description
The five volume set LNCS 10960 until 10964 constitutes the refereed proceedings of the 18th International Conference on Computational Science and Its Applications, ICCSA 2018, held in Melbourne, Australia, in July 2018. Apart from the general tracks, ICCSA 2018 also includes 34 international workshops in various areas of computational sciences, ranging from computational science technologies, to specific areas of computational sciences, such as computer graphics and virtual reality. The total of 265 full papers and 10 short papers presented in the 5-volume proceedings set of ICCSA 2018, were carefully reviewed and selected from 892 submissions.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 348
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Book Description
Author: Hans-Görg Roos
Publisher: Springer Science & Business Media
ISBN: 3540344675
Category : Mathematics
Languages : en
Pages : 599
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Book Description
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Author: Graham De Vahl Davis
Publisher:
ISBN: 9780909287375
Category : Fluid dynamics
Languages : en
Pages : 21
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Book Description
