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The development of high-order accurate numerical discretization
techniques for irregular domains and meshes is often cited as one
of the remaining chal lenges facing the field of computational
fluid dynamics. In structural me chanics, the advantages of
high-order finite element approximation are widely recognized. This
is especially true when high-order element approximation is
combined with element refinement (h-p refinement). In computational
fluid dynamics, high-order discretization methods are infrequently
used in the com putation of compressible fluid flow. The hyperbolic
nature of the governing equations and the presence of solution
discontinuities makes high-order ac curacy difficult to achieve.
Consequently, second-order accurate methods are still predominately
used in industrial applications even though evidence sug gests that
high-order methods may offer a way to significantly improve the
resolution and accuracy for these calculations. To address this
important topic, a special course was jointly organized by the
Applied Vehicle Technology Panel of NATO's Research and Technology
Organization (RTO), the von Karman Institute for Fluid Dynamics,
and the Numerical Aerospace Simulation Division at the NASA Ames
Research Cen ter. The NATO RTO sponsored course entitled "Higher
Order Discretization Methods in Computational Fluid Dynamics" was
held September 14-18,1998 at the von Karman Institute for Fluid
Dynamics in Belgium and September 21-25,1998 at the NASA Ames
Research Center in the United States."
As computational fluid dynamics (CFD) is applied to ever more
demanding fluid flow problems, the ability to compute numerical
fluid flow solutions to a user specified tolerance as well as the
ability to quantify the accuracy of an existing numerical solution
are seen as essential ingredients in robust numerical simulation.
Although the task of accurate error estimation for the nonlinear
equations of CFD seems a daunting problem, considerable effort has
centered on this challenge in recent years with notable progress
being made by the use of advanced error estimation techniques and
adaptive discretization methods. To address this important topic, a
special course wasjointly organized by the NATO Research and
Technology Office (RTO), the von Karman Insti tute for Fluid
Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored
course entitled "Error Estimation and Solution Adaptive
Discretization in CFD" was held September 10-14, 2002 at the NASA
Ames Research Center and October 15-19, 2002 at the von Karman
Institute in Belgium. During the special course, a series of
comprehensive lectures by leading experts discussed recent advances
and technical progress in the area of numerical error estimation
and adaptive discretization methods with spe cific emphasis on
computational fluid dynamics. The lecture notes provided in this
volume are derived from the special course material. The volume con
sists of 6 articles prepared by the special course lecturers."
This book considers recent developments in numerical error estimation and adaptive discretization for finite element and finite volume methods with particular attention given to discretization methods used frequently in computational fluid dynamics. The volume consists of six detailed articles by leading specialists covering a range of topics including a posteriori error estimation of functionals, one- and two-sided error bounds, error indicators for ad aptivity, and nd geometrical aspects of adaptive mesh refinement. This book should be of interest to readers actively working in the field as well as readers seeking a comprehensive introduction to the topic.
Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.
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