This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

From the reviews of the first edition: "This book is directed to graduate students and research workers interested in the numerical solution of problems of fluid dynamics, primarily those arising in high speed flow. ...The book is well arranged, logically presented and well illustrated. It contains several FORTRAN programms with which students could experiment ... It is a practical book, with emphasis on methods and their implementation. It is an excellent text for the fruitful research area it covers, and is highly recommended." Journal of Fluid Mechanics #1 From...

The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well.

Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems.

The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial...

The domain of inverse problems has experienced a rapid expansion, driven by the increase in computing power and the progress in numerical modeling. When I started working on this domain years ago, I became somehow fr- tratedtoseethatmyfriendsworkingonmodelingwhereproducingexistence, uniqueness, and stability results for the solution of their equations, but that I was most of the time limited, because of the nonlinearity of the problem, to provethatmyleastsquaresobjectivefunctionwasdi?erentiable....Butwith my experience growing, I became convinced that, after the inverse problem has been...

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors' interests in incompressible vortex-dominated ?ows and compressible ?ows at low...

The ?nite element method is one of the major tools used in the numerical solution of partial di?erential equations. This book o?ers a fundamental and practical introduction to the method, its variants, and their applications. In presenting the material, I have attempted to introduce every concept in the simplest possible setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. The book is based on the material that I have used in a graduate course at Southern Methodist University for several years. Part of the material was...

The field of computational fluid dynamics (CFD) has already had a significant impact on the science and engineering of fluid dynamics, ranging from a role in aircraft design to enhancing our understanding of turbulent flows. It is thus not surprising that there exist several excellent books on the subject. We do not attempt to duplicate material which is thoroughly covered in these books. In particular, our book does not describe the most recent developments in algorithms, nor does it give any instruction with respect to programming. Neither turbulence modelling nor grid generation are...

This book addresses hybrid simulation of plasmas; it is aimed at developing insight into the essence of plasma behavior. Major current applications are to astrophysical and space plasmas. Some applications are connected with active experiments in space. However, hybrid simulations are also being used to gain an understanding of basic plasma phenomena such as particle acceleration by shocks, magnetic field reconnect ion in neutral current sheets, generation of waves by beams, mass loading of the supersonic flow by heavy pickup ions and the dynamics of tangential discontinuities. Such...

This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details...

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.