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.

Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.