A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. The book begins by recounting the events that lead to our understanding of the theory of shock waves and the early developments related to their computation. After presenting the main shock-fitting ideas in the context of a simple scalar equation, the author applies Colombeau's theory of generalized functions to the Euler equations to demonstrate how the theory recovers well-known results and to provide an in-depth understanding of the nature of jump conditions. He then extends the shock-fitting concepts previously discussed to the one-dimensional and quasi-one-dimensional Euler equations as well as two-dimensional flows. The final chapter explores existing and future developments in shock-fitting methods within the framework of unstructured grid methods. Throughout the text, the techniques developed are illustrated with numerous examples of varying complexity. On the accompanying downloadable resources, MATLAB (R) codes serve as concrete examples of how to implement the ideas discussed in the book.

This volume contains the proceedings of the first ICASE/LaRC Work shop on Computational Electromagnetics and Its Applications conducted by the Institute for Computer Applications in Science and Engineering and NASA Langley Research Center. We had several goals in mind when we decided, jointly with the Elec tromagnetics Research Branch, to organize this workshop on Computa tional Electromagnetics ( CEM). Among our goals were a desire to obtain an overview of the current state of CEM, covering both algorithms and ap plications and their effect on NASA's activities in this area. In addition, we wanted to provide an attractive setting for computational scientists with expertise in other fields, especially computational fluid dynamics (CFD), to observe the algorithms and tools of CEM at work. Our expectation was that scientists from both fields would discover mutually beneficial inter connections and relationships. Another goal was to learn of progress in solution algorithms for electromagnetic optimization and design problems; such problems make extensive use of field solvers and computational effi ciency is at a premium. To achieve these goals we assembled the renowned group of speakers from academia and industry whose talks are contained in this volume. The papers are printed in the same order in which the talks were pre sented at the meeting. The first paper is an overview of work currently being performed in the Electromagnetic Research Branch at the Langley Research Center."

In this volume, designed for engineers and scientists working in the area of Computational Fluid Dynamics (CFD), experts offer assessments of the capabilities of CFD, highlight some fundamental issues and barriers, and propose novel approaches to overcome these problems. They also offer new avenues for research in traditional and non-traditional disciplines. The scope of the papers ranges from the scholarly to the practical. This book is distinguished from earlier surveys by its emphasis on the problems facing CFD and by its focus on non-traditional applications of CFD techniques. There have been several significant developments in CFD since the last workshop held in 1990 and this book brings together the key developments in a single unified volume.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics, ' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely."

Over the last decade, the role of computational simulations in all aspects of aerospace design has steadily increased. However, despite the many advances, the time required for computations is far too long. This book examines new ideas and methodologies that may, in the next twenty years, revolutionize scientific computing. The book specifically looks at trends in algorithm research, human computer interface, network-based computing, surface modeling and grid generation and computer hardware and architecture. The book provides a good overview of the current state-of-the-art and provides guidelines for future research directions. The book is intended for computational scientists active in the field and program managers making strategic research decisions.

An outstanding feature of this book is a collection of state-of-the-art reviews written by leading researchers in the nanomechanics of carbon nanotubes, nanocrystalline materials, biomechanics and polymer nanocomposites. The structure and properties of carbon nanotubes, polycrystalline metals, and coatings are discussed in great details. The book is an exceptional resource on multi-scale modelling of metals, nanocomposites, MEMS materials and biomedical applications. An extensive bibliography concerning all these topics is included. Highlights on bio-materials, MEMS, and the latest multi-scale methods (e.g., molecular dynamics and Monte Carlo) are presented. Numerous illustrations of inter-atomic potentials, nanotube deformation and fracture, grain rotation and growth in solids, ceramic coating structures, blood flows and cell adhesion are discussed.
This book provides a comprehensive review of latest developments in the analysis of mechanical phenomena in nanotechnology and bio-nanotechnology.

An outstanding feature of this book is a collection of state-of-the-art reviews written by leading researchers in the nanomechanics of carbon nanotubes, nanocrystalline materials, biomechanics and polymer nanocomposites. The structure and properties of carbon nanotubes, polycrystalline metals, and coatings are discussed in great details. The book is an exceptional resource on multi-scale modelling of metals, nanocomposites, MEMS materials and biomedical applications. An extensive bibliography concerning all these topics is included. Highlights on bio-materials, MEMS, and the latest multi-scale methods (e.g., molecular dynamics and Monte Carlo) are presented. Numerous illustrations of inter-atomic potentials, nanotube deformation and fracture, grain rotation and growth in solids, ceramic coating structures, blood flows and cell adhesion are discussed.
This book provides a comprehensive review of latest developments in the analysis of mechanical phenomena in nanotechnology and bio-nanotechnology.

Over the last decade, the role of computational simulations in all aspects of aerospace design has steadily increased. However, despite the many advances, the time required for computations is far too long. This book examines new ideas and methodologies that may, in the next twenty years, revolutionize scientific computing. The book specifically looks at trends in algorithm research, human computer interface, network-based computing, surface modeling and grid generation and computer hardware and architecture. The book provides a good overview of the current state-of-the-art and provides guidelines for future research directions. The book is intended for computational scientists active in the field and program managers making strategic research decisions.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics, ' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely."

This publication documents the proceedings of the first Workshop on Computational Electromagnetics (CEM) and Applications, hosted by the Institute for Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center, Hampton, Virginia, 29-31 May, 1996, and attended by approximately 70 people from academia, government laboratories, and industry. ICASE's charter mission in 1972 remains today - to explore novel computer environments (vector in the 1970s; parallel in the 1990s) for scientific computing. These proceedings provide a necessary foundation for symposia in computational electromagnetics for future aerospace applications. The objectives of this CEM Workshop were to provide a forum for many of the leaders of the community to assess the state of CEM technology and to discuss areas of research for future programmatic planning activities. Workshop sessions included topics on optimization, industrial applications, algorithms, and a special panel session was provided during which issues were discussed and future research areas were identified. Hopefully, this publication will stimulate and improve communication among multidisciplinary researchers as well as highlighting several CEM areas that need improvement - especially for highly challenging problems. The two most important criteria in the selection of speakers for the workshop were their substantial contribution to large-scale CEM problems and their ability to articulate the issues confronting the CEM research community. Based on the results obtained, it is anticipated that this publication will be useful to government, industry, and university researchers to plan future research tasks in CEM analyticalmethods and applications.

In this volume, designed for engineers and scientists working in the area of Computational Fluid Dynamics (CFD), experts offer assessments of the capabilities of CFD, highlight some fundamental issues and barriers, and propose novel approaches to overcome these problems. They also offer new avenues for research in traditional and non-traditional disciplines. The scope of the papers ranges from the scholarly to the practical. This book is distinguished from earlier surveys by its emphasis on the problems facing CFD and by its focus on non-traditional applications of CFD techniques. There have been several significant developments in CFD since the last workshop held in 1990 and this book brings together the key developments in a single unified volume.