Incompressible Flow and the Finite Element Method, 2 Volume Set

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.

1. Glossary of Abbreviations 2. Preface and Introduction 3. The Navier-Stokes Equations Notational Introduction The Continuum Equations Alternate Forms of the Viscous Term Alternate Forms of the Non-Linear Term Derived Equations Alternate Statements of the NS Equations Special Cases of Interest Boundary Conditions Initial Conditions (and Well-Posedness) Interim Summary Global Conservation Laws Weak Form of the PDEhod Variational Principles for Potential and Stokes Flow Solution Methods for the Semi_Discretized Time-Dependent (and Steady) Equations Aliasing and Aliasing Instability, Linear and Non-Linear A New Look at Two Old Finite Difference Methods Numerical Example Closure: Some Additional Remarks on the Pressure 4. Derived Quantities Introduction Two Dimensions Three Dimensions Appendix 1 Some Element Matrix Appendix 2 Further Comparison of Finite Elements and Finite Volumes Appendix 3 Projections, Orthagonal and Not and Projection Methods References Author Index Subject Index