An interactive programming environment for solving partial differential equations using adaptive grids (with application to flame-flow interaction problems).
Item
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Title
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An interactive programming environment for solving partial differential equations using adaptive grids (with application to flame-flow interaction problems).
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Identifier
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AAI9218245
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identifier
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9218245
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Creator
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Kozlovsky, Gregory.
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Contributor
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Co-Advisers: Octavio Betancourt | Gregory Sivashinsky
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Date
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1992
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Language
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English
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Publisher
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City University of New York.
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Subject
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Computer Science | Engineering, Mechanical | Physics, Fluid and Plasma
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Abstract
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In this work we investigate software tools and numerical methods for modeling physical phenomena with high local resolution. The following interrelated issues are addressed: adaptive grids, formulation of the finite element method on adaptive grids, and programming environments for numerical software development and scientific visualization.;We introduce a class of adaptive grids called consistent recursive grids and study its properties. Algorithms for refinement, unrefinement, grid traversal, and nearest node search are developed. Data structures for computer implementation of such grids are proposed.;A version of the finite element method specifically designed for consistent recursive grids is described. This version uses discontinuous trial functions in order to simplify matrix generation on interfaces of computational cells of different sizes.;We identify shortcomings of existing tools for numerical software development and introduce the concept of geometric debugging. We present an interactive programming environment which provides a way to connect geometrically based understanding with underlying data structures. The programming environment includes an integrated library of functions for dynamic recursive grids and an integrated interactive graphics module.;Finally, we address application of the developed software to flame-flow interaction problems of interest to combustion scientists, and present computational results.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
