The discontinuous finite element method (also known as the
discontinuous Galerkin method) embodies the advantages of both
finite element and finite difference methods. It can be used in
convection-dominant applications while maintaining geometric
flexibility and higher local approximations throught the use of
higher-order elements. Element-by element connection propagates the
effect of boundary conditions and the local formulation obviates
the need for global matrix assembly. All of this adds up to a
method which is not unduly memory-intensive and uniquely useful for
working with computational dynamics, heat transfer and fluid flow
calculations.
Discontinuous Finite Elements in Fluid Dynamics and Heat
Transfer offers its readers a systematic and practical introduction
to the discontinuous finite element method. It moves from a brief
review of the fundamental laws and equations governing thermal and
fluid systems, through a discussion of different approaches to the
formulation of discontinuous finite element solutions for boundary
and initial value problems, to their applicaton in a variety of
thermal-system and fluid-related problems, including:
- heat conduction problems;
- convection-dominant problems;
- compressible and incompressible flows;
- external radiation problems;
- internal radiation and radiative transfer;
- free- and moving-boundary problems;
- micro- and nanoscale heat transfer and fluid flow;
- thermal fluid flow under the influence of applied magnetic
fields.
Mesh generation and adaptivity, parellelization algorithms and a
priori and a posteriori error analysis are also introduced
andexplained, rounding out a comprehensive review of the
subject.
Each chapter features worked examples and exercises illustrating
situations ranging from simple benchmarks to practical engineering
questions.
This textbook is written to form the foundations of senior
undergraduate and graduate learning and also provides scientists,
applied mathematicians and research engineers with a thorough
treatment of basic concepts, specific techniques and methods for
the use of discontinuous Galerkin methods in computational fluid
dynamics and heat transfer applications.
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