Time-Integration Algorithms for the Computer Treatment of the Horizontal Advection in Air Pollution Models PDF Download
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Author: Zahari Zlatev
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
The horizontal advection is one of the most important physical processes in an air pollution model. While it is clear how to describe mathematically this process, the computer treatment of the arising first-order partial differential equation (PDE) causes great difficulties. It is assumed that the spatial derivatives in this equation are discretized either by finite differences or by finite elements. This results in a very large system of ordinary differential equations (ODEs). The numerical treatment of this system of ODEs is based on the application of a set of predictor-corrector (PC) schemes with different absolute stability properties. The PC schemes can be varied during the time-integration. Schemes, which are computationally cheaper, are selected when the stability requirements are not stringent. If the stability requirements are stringent, then schemes that are more time-consuming, but also have better stability properties, are chosen. Some norms of the wind velocity vectors are calculated and used in the check of the stability requirements. Reductions of the time-step size are avoided (or, at least, reduced considerably) when the PC schemes are appropriately varied. This leads to an increase of the efficiency of the computations in the treatment of large-scale air pollution models. The procedure is rather general and can also be used in the computer treatment of other large-scale problems arising in different fields of science and engineering.
Author: Zahari Zlatev
Publisher:
ISBN:
Category :
Languages : en
Pages : 12
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Book Description
The horizontal advection is one of the most important physical processes in an air pollution model. While it is clear how to describe mathematically this process, the computer treatment of the arising first-order partial differential equation (PDE) causes great difficulties. It is assumed that the spatial derivatives in this equation are discretized either by finite differences or by finite elements. This results in a very large system of ordinary differential equations (ODEs). The numerical treatment of this system of ODEs is based on the application of a set of predictor-corrector (PC) schemes with different absolute stability properties. The PC schemes can be varied during the time-integration. Schemes, which are computationally cheaper, are selected when the stability requirements are not stringent. If the stability requirements are stringent, then schemes that are more time-consuming, but also have better stability properties, are chosen. Some norms of the wind velocity vectors are calculated and used in the check of the stability requirements. Reductions of the time-step size are avoided (or, at least, reduced considerably) when the PC schemes are appropriately varied. This leads to an increase of the efficiency of the computations in the treatment of large-scale air pollution models. The procedure is rather general and can also be used in the computer treatment of other large-scale problems arising in different fields of science and engineering.
Author: Zahari Zlatev
Publisher: Springer Science & Business Media
ISBN: 9401103119
Category : Science
Languages : en
Pages : 367
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Book Description
"Models are often the only way of interpreting measurements to in vestigate long-range transport, and this is the reason for the emphasis on them in many research programs". B. E. A. Fisher: "A review of the processes and models of long-range transport of air pollutants", Atmospheric Environment, 17(1983), p. 1865. Mathematical models are (potentially, at least) powerful means in the efforts to study transboundary transport of air pollutants, source-receptor relationships and efficient ways of reducing the air pollution to acceptable levels. A mathematical model is a complicated matter, the development of which is based on the use of (i) various mechanisms describing mathematically the physical and chemical properties of the studied phenomena, (ii) different mathematical tools (first and foremost, partial differenti al equations), (iii) various numerical methods, (iv) computers (especially, high-speed computers), (v) statistical approaches, (vi) fast and efficient visualization and animation techniques, (vii) fast methods for manipulation with huge sets of data (input data, intermediate data and output data).
Author: Svetozar D. Margenov
Publisher: Springer
ISBN: 3540453466
Category : Computers
Languages : en
Pages : 500
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Book Description
This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Large-Scale Scientific Computing, LSSC 2001, held in Sozopol, Bulgaria, in June 2001. The 7 invited full papers and 45 selected revised papers were carefully reviewed for inclusion in the book. The papers are organized in topical sections on robust preconditioning algorithms, Monte-Carlo methods, advanced programming environments for scientific computing, large-scale computations in air pollution modeling, large-scale computations in mechanical engineering, and numerical methods for incompressible flow.
Author: Zahari Zlatev
Publisher: Springer Science & Business Media
ISBN: 9780792356783
Category : Computers
Languages : en
Pages : 414
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Book Description
Proceedings of the NATO Advanced Research Workshop, Sofia, Bulgaria, 6-10 July 1998
Author: Jan G. Verwer
Publisher:
ISBN:
Category : Air
Languages : en
Pages : 58
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Book Description
Abstract: "Due to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [formula] from the field of air pollution modelling. This has led to the use of special time integration techniques. This paper is devoted to a survey of such techniques, encompassing stiff chemistry solvers, positive advection schemes, time or operator splitting, implicit-explicit methods and approximate matrix factorization solutions. Of great importance in practice is high performance computing due to the huge problem scales, in particular for global models. We will therefore also report on experiences with vector/parallel shared memory and massively parallel distributed memory architectures and clusters of workstations. The survey is not entirely unique to air pollution models and biased towards work done at CWI over approximately the last 5 years."
Author: J. M. Baldasano
Publisher: Computational Mechanics
ISBN: 9781853123603
Category : Nature
Languages : en
Pages : 616
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Book Description
The last decade has shown an increase in public and government concern around environmental issues due to air pollution, in particular those generated by man-made processes seeking the comfort of modern society. Atmospheric pollution consists of the adverse effects on the environment of a variety of substances (contaminants) emitted into the atmosphere by natural and man-made processes. These phenomena are complicated by the fact that an apparently inert contaminant can be transformed by chemical reaction into an adverse one, during its transport through the atmosphere.
Author: I. Dimov
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
The air pollution, and especially the reduction of the air pollution to some acceptable levels, is an important environmental problem, which will become even more important in the next 10-20 years. This problem can successfully be studied only when high-resolution comprehensive models are developed and used on a routinely basis. However, such models are very time-consuming, also when modern high-speed computers are available. Indeed, if an air pollution model is to be applied on a large space domain by using fine grids, then its discretization will always lead to huge computational problems. Assume, for example, that the space domain is discretized by using a (480×480) grid and that the number of chemical species studied by the model is 35. Then several systems of ordinary differential equations containing 8064000 equations have to be treated at every time-step (the number of time-steps being typically several thousand). If a three-dimensional version of the same air pollution model is to be used, then the above figure must be multiplied by the number of layers. It is extremely difficult to treat such large computational problems; even when the fastest computers that are available at present are used.There is an additional great difficulty which is very often underestimated (or even neglected) when large application packages are moved from sequential computers to modern parallel machines. The high-speed computers have normally a very complicated memory architecture and, therefore, the task of producing an efficient code for the particular high-speed computer that is available is both extremely hard and very laborious.The use of standard parallelization tools in the solution of the problems sketched above is discussed in this paper. Results obtained on different types of parallel computers are given. It is demonstrated that the new efficient parallel algorithms allow us to solve more problems and bigger problems.
Author: Khoi Huu Nguyen
Publisher:
ISBN:
Category : Air quality
Languages : en
Pages : 102
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Book Description
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: P. Zannetti
Publisher: Springer Science & Business Media
ISBN: 147574465X
Category : Science
Languages : en
Pages : 448
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Book Description
Finishing this book is giving me a mixture of relief, satisfaction and frus tration. Relief, for the completion of a project that has taken too many of my evenings and weekends and that, in the last several months, has become almost an obsession. Satisfaction, for the optimistic feeling that this book, in spite of its many shortcomings and imbalances, will be of some help to the air pollution scientific community. Frustration, for the impossibility of incorporating newly available material that would require another major review of several key chap ters - an effort that is currently beyond my energies but not beyond my desires. The first canovaccio of this book came out in 1980 when I was invited by Computational Mechanics in the United Kingdom to give my first Air Pollution Modeling course. The course material, in the form of transparencies, expanded, year after year, thus providing a growing working basis. In 1985, the ECC Joint Research Center in Ispra, Italy, asked me to prepare a critical survey of mathe matical models of atmospheric pollution, transport and deposition. This support gave me the opportunity to prepare a sort of "first draft" of the book, which I expanded in the following years.
