Viscous Incompressible Flow

Chapter 1: Fundamentals of Low Reynolds Number Viscous Incompressible Flow Dimensionless analysis of the equations governing the flow of an incompressible Newtonian fluid; Boundary and initial conditions for the flow on an incompressible Newtonian fluid; General properties of Stokes flows; The generalized Lorentz reciprocal identity for Stokes flows; General properties of unsteady Stokes flows; Green's formulas and the reciprocal identity for unsteady Stokes flows; Oseen's flow Chapter 2: The Singularity Method for Low Reynolds Number Viscous Incompressible Flows Green's function of the Stokes flow due to a point force; Singularities of Stokes flows; Computation of Stokes flows by the singularity method; Fundamental solutions of unsteady Stokes flows; Computation of unsteady Stokes flows by the singularity method; The fundamental solution of Oseen's flow; Fundamental solutions of generalized unsteady Oseen and Stokes flows Chapter 3: The Theory of Hydrodynamic Potentials with Application to Low Reynolds Number Viscous Incompressible Flows Boundary integral representations for the velocity fields of Stokes and Oseen flows: Boundary integral representation for the pressure field of an unbounded Stokes flow; The generalized Faxen laws for the total force and torque on a particle; Basic properties of the hydrodynamic potentials; Existence and uniqueness results for the Stokes system; Boundary integral representations for the velocity and pressure fields of unsteady Stokes flows; Existence and uniqueness results for the unsteady Stokes system Chapter 4: Boundary Integral Methods for Steady and Unsteady Stokes Flows The boundary element method (BEM); Power and Miranda's method for Stokes flow past a solid particle of arbitrary shape in an unbounded domain; Boundary integral representations for Stokes flow past several solid particles in an unbounded domain; Compound double-layer representations for Stokes flows in bounded domains; A compound double-layer representation for the two-dimensional Stokes flow problem in exterior domains; The method of matched asymptotic expansions for low Reynolds number flow past a cylinder of arbitrary cross-section; Asymptotic analysis of low Reynolds number viscous incompressible flow past a cylindrical body; A compound double-layer representation for the two-dimensional Stokes flow due to the motion of a solid particle in a half-plane; Compound double-layer representations for the two-dimensional Stokes flow past or due to the motion of a cylinder in a channel; Boundary integral method for an oscillatory Stokes flow in the presence of a solid particle Chapter 5: Boundary Integral Formulations for Linearized Viscous Flows in the Presence of Interfaces A boundary integral formulation for the deformation of a viscous drop in an extensional flow; A boundary integral formulation for Stokes flow past a solid sphere and a viscous drop; A boundary integral formulation for slow viscous flow in a bounded fluid region containing a solid particle; A boundary integral method for Stokes flow in a bounded region containing air bubbles