Numerical Solution of the Incompressible Navier-Stokes Equations [Hardcover]

This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.1 The incompressible Navier-Stokes equations.- 1.1 Introduction.- 1.2 Incompressible Navier-Stokes equations.- 1.3 Organization of the book.- 1.4 Some references.- 2 Nonprimitive variable formulations in 2D.- 2.1 Introduction.- 2.2 Vorticity-stream function equations.- 2.3 Biharmonic formulation.- 2.4 Coupled vorticity-stream function equations.- 2.5 Vorticity integral conditions.- 2.5.1 Green identities.- 2.5.2 Vorticity integral conditions.- 2.5.3 What the integral conditions are not.- 2.6 Split vorticity-stream function equations.- 2.7 One-dimensional integral conditions.- 2.8 Orthogonal projection operator.- 2.9 Factorized vorticity-stream function problem.- 2.10 Numerical schemes: local discretizations.- 2.10.1 Boundary vorticity formula methods.- 2.10.2 Decomposition scheme.- 2.10.3 Glowinski-Pironneau method.- 2.10.4 Discretization of the ló{