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This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications. Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
List of contents
Introduction.- 1. Vectors and Curvilinear Coordinates.- 2. Main Concept of Continuum Mechanics.- 3. Main Equations of Continuum Mechanics.- 4. Classical Model of Continuum Mechanics.- 5. Hydrostatics and Theory of Elasticity.- 6. Mathematical Model of the Slurry Flow in Hydraulic Crack in the Bed.- 7. Mathematical Model of Non-Stationary Single- and Two-Phase Flows in Pipes.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- References.- Author Index.- Subject Index.
About the author
Vladimir Markovich Entov (1937-2008) worked at the Institute for Problems in Mechanics of the Soviet Academy of Science fom 1971 onwards. Since 1983 he also was Professor of Applied Mathematics and Computer Modeling at the Moscow Institute of Oil and Gas (now known as the Gubkin Russian State University of Oil and Gas). In later years he was involved in research and teaching activity at Institut de Physique du Globe de Paris, the universities of Cambridge and Oxford, and the University of Stanford and served as member of the editorial board of the European Journal of Applied Mathematics.
Summary
This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications. Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
