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Addressing students and researchers as well as Computational Fluid
Dynamics practitioners, this book is the most comprehensive review
of high-resolution schemes based on the principle of Flux-Corrected
Transport (FCT). The foreword by J.P. Boris and historical note by
D.L. Book describe the development of the classical FCT methodology
for convection-dominated transport problems, while the design
philosophy behind modern FCT schemes is explained by S.T. Zalesak.
The subsequent chapters present various improvements and
generalizations proposed over the past three decades.
In this new edition, recent results are integrated into existing
chapters in order to describe significant advances since the
publication of the first edition. Also, 3 new chapters were added
in order to cover the following topics: algebraic flux correction
for finite elements, iterative and linearized FCT schemes, TVD-like
flux limiters, acceleration of explicit and implicit solvers, mesh
adaptation, failsafe limiting for systems of conservation laws,
flux-corrected interpolation (remapping), positivity preservation
in RANS turbulence models, and the use of FCT as an implicit
subgrid scale model for large eddy simulations.
Addressing students and researchers as well as Computational Fluid
Dynamics practitioners, this book is the most comprehensive review
of high-resolution schemes based on the principle of Flux-Corrected
Transport (FCT). The foreword by J.P. Boris and historical note by
D.L. Book describe the development of the classical FCT methodology
for convection-dominated transport problems, while the design
philosophy behind modern FCT schemes is explained by S.T. Zalesak.
The subsequent chapters present various improvements and
generalizations proposed over the past three decades.
In this new edition, recent results are integrated into existing
chapters in order to describe significant advances since the
publication of the first edition. Also, 3 new chapters were added
in order to cover the following topics: algebraic flux correction
for finite elements, iterative and linearized FCT schemes, TVD-like
flux limiters, acceleration of explicit and implicit solvers, mesh
adaptation, failsafe limiting for systems of conservation laws,
flux-corrected interpolation (remapping), positivity preservation
in RANS turbulence models, and the use of FCT as an implicit
subgrid scale model for large eddy simulations.
High-order numerical methods for hyperbolic conservation laws do
not guarantee the validity of constraints that physically
meaningful approximations are supposed to satisfy. The finite
volume and finite element schemes summarized in this book use
limiting techniques to enforce discrete maximum principles and
entropy inequalities. Spurious oscillations are prevented using
artificial viscosity operators and/or essentially nonoscillatory
reconstructions.An introduction to classical nonlinear
stabilization approaches is given in the simple context of
one-dimensional finite volume discretizations. Subsequent chapters
of Part I are focused on recent extensions to continuous and
discontinuous Galerkin methods. Many of the algorithms presented in
these chapters were developed by the authors and their
collaborators. Part II gives a deeper insight into the mathematical
theory of property-preserving numerical schemes. It begins with a
review of the convergence theory for finite volume methods and ends
with analysis of algebraic flux correction schemes for finite
elements. In addition to providing ready-to-use algorithms, this
text explains the design principles behind such algorithms and
shows how to put theory into practice. Although the book is based
on lecture notes written for an advanced graduate-level course, it
is also aimed at senior researchers who develop and analyze
numerical methods for hyperbolic problems.
This informal introduction to computational fluid dynamics and
practical guide to numerical simulation of transport phenomena
covers the derivation of the governing equations, construction of
finite element approximations, and qualitative properties of
numerical solutions, among other topics. To make the book
accessible to readers with diverse interests and backgrounds, the
authors begin at a basic level and advance to numerical tools for
increasingly difficult flow problems, emphasizing practical
implementation rather than mathematical theory. Finite Element
Methods for Computational Fluid Dynamics: * Explains the basics of
the finite element method (FEM) in the context of simple model
problems, illustrated by numerical examples. * Comprehensively
reviews stabilization techniques for convection-dominated transport
problems, introducing the reader to streamline diffusion methods,
Petrov-Galerkin approximations, Taylor-Galerkin schemes,
flux-corrected transport algorithms, and other nonlinear
high-resolution schemes.* Covers Petrov-Galerkin stabilization,
classical projection schemes, Schur complement solvers, and the
implementation of the k-epsilon turbulence model in its
presentation of the FEM for incompressible flow problems.*
Ddescribes the open-source finite element library ELMER, which is
recommended as a software development kit for advanced applications
in an online component.
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