Incompressible Flow and the Finite Element Method: Advection-diffusion and Isothermal Laminar Flow - Hardcover

Gresho, PM

Hardcover

ISBN 10: 0471967890 ISBN 13: 9780471967897

Publisher: Wiley–Blackwell, 1998

Synopsis

This comprehensive reference work covers all the important details regarding the application of the finite element method to incompressible flows. It addresses the theoretical background and the detailed development of appropriate numerical methods applied to the solution of a wide range of incompressible flows, beginning with extensive coverage of the advection–diffusion equation in volume one. For both this equation and the equations of principal interest – the Navier–Stokes equations, covered in detail in volume two – detailed discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the time–dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well–posedness. The important role played by the pressure, so confusing in the past, is carefully explained.
Together, this two volume work explains and emphasizes consistency in six areas:
⋅ consistent mass matrix
⋅ consistent pressure Poisson equation
⋅ consistent penalty methods
⋅ consistent normal direction
⋅ consistent heat flux
⋅ consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.

About this title

From the Back Cover

This comprehensive two volume reference work is devoted to the important details regarding the application of the finite element method to incompressible flows, addressing the theoretical background and the detailed development of appropriate numerical methods applied to their solution. Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advection–diffusion equation. In addition, for both this equation and the equations of principal interest – the Navier–Stokes equations – (covered in detail in Volume Two), a discussion of both the continuous and discrete equations is presented. Also addressed are explanations of how to properly march the time–dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are thoroughly described and discussed, including well–posedness. The important role played by the pressure, so confusing in the past, is carefully explained. Together, this two volume work explains and emphasizes consistency in six areas:
∗ consistent mass matrix
∗ consistent pressure Poisson equation
∗ consistent penalty methods
∗ consistent normal direction
∗ consistent heat flux
∗ consistent forces
Fully indexed and referenced

Synopsis

This text deals with the applications of the finite element method to incompressible flows. Volume One addresses the theoretical background and the methods development to the solution of a wide range of incompressible flows. Volume Two due May 1997) will be practice orientated and will address the simulation of the numerical solutions of the Navier-Stoke equations via the finite element method. The two volumes can be used as self-teaching tutorials for students at graduate level as they include worked exercises and applications and sample results of computer simulations. They should also appeal to practising engineers working with advection-diffusion incompressible flow and incompressible FEM fluid mechanics.

Edition details

• Publisher: Wiley–Blackwell
• Publication date: 1998
• ISBN 10: 0471967890
• ISBN 13: 9780471967897
• Binding: Hardcover
• Language: English
• Number of pages: 1044