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Author: William Schiesser Publisher: CRC Press ISBN: 1000001040 Category : Mathematics Languages : en Pages : 182
Book Description
Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.
Author: William Schiesser Publisher: CRC Press ISBN: 1000001040 Category : Mathematics Languages : en Pages : 182
Book Description
Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.
Author: Ben Q. Li Publisher: Springer Science & Business Media ISBN: 1846282055 Category : Technology & Engineering Languages : en Pages : 587
Book Description
Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.
Author: John Crank Publisher: Oxford University Press, USA ISBN: Category : Mathematics Languages : en Pages : 438
Book Description
Here is a wide-ranging, comprehensive account of the mathematical formulation of problems involving free boundaries as they occur in such diverse areas as hydrology, metallurgy, chemical engineering, soil science, molecular biology, materials science, and steel and glass production. Many newmethods of solution are discussed, including modern computer techniques which address multidimensional, multiphase practical problems.
Author: Subrata Kumar Chakrabarti Publisher: WIT Press ISBN: 1845640721 Category : Science Languages : en Pages : 369
Book Description
Publishing papers presented at the Fourth International Conference on Fluid Structure Interactions, this book features contributions from experts specialising in this field on new ideas and the latest techniques. A valuable addition to this successful series and will be of great interest to mechanical and structural engineers, offshore engineers, earthquake engineers, naval engineers and any other experts involved in topics related to fluid structure interaction. Topics covered include: Hydrodynamic Forces; Response of Structures including Fluid Dynamic; Offshore Structure and Ship Dynamics; Fluid Pipeline Interactions; Structure Response to Serve Shock and Blast Loading; Vortex Shedding and Flow Induced Vibrations; Cavitations Effects in Turbo Machines and Pumps; Wind Effects on Bridges and Tall Structures; Mechanics of Cables, Rivers and Moorings; Building Biofluids and Biological Tissue Interaction Problems in CFD; Experimental Studies and Validation; Vibrations and Noise; Free Surface Flows and Moving Boundary Problems.
Author: A. A. Mammoli Publisher: Computational and Experimental ISBN: 9781853129872 Category : Technology & Engineering Languages : en Pages : 0
Book Description
In these proceedings from the November 2003 conference, contributors consider the computational modeling of a continuum, where the positions of its borders or interphase boundaries must also be found. They examine theory, models, methods, and applications in different research perspectives. Topics include boundary tracking, fluid structure interactions, flow-through porous media, free surface flow, phase change, phase interface phenomena, and advanced computational methods in two and three dimensions. Applications include microelectronics, medicine, and materials science. The U.S. office of WIT Press is Computational Mechanics. Annotation : 2004 Book News, Inc., Portland, OR (booknews.com).
Author: Fengshan Yang Publisher: Nova Publishers ISBN: 9781600219764 Category : Mathematics Languages : en Pages : 386
Book Description
This book presents new research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. It includes heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimisation; finite volume, finite element, and boundary element procedures; decision sciences in an industrial and manufacturing context; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
Author: Pierluigi Colli Publisher: Birkhäuser ISBN: 3034878931 Category : Mathematics Languages : en Pages : 342
Book Description
Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.
Author: William Schiesser
Author: William Schiesser
Author: Ben Q. Li
Author: John Crank
Author: Adrian Muntean
Author: B. Šarler
Author: National Research Council
Author: Subrata Kumar Chakrabarti
Author: A. A. Mammoli
Author: Fengshan Yang
Author: Pierluigi Colli