Boundary Integral Methods in Fluid Mechanics

Part 1 Introduction to fluid mechanics: basic conservation laws approximate forms of the governing equations special forms of the governing equations. Part 2 Integral equation theory: classification of integral equations method of successive approximations integral equations with degenerate kernels general case of Fredholm's equation systems of integral equations. Part 3 Potential theory: basic concepts of potential theory indirect formulation regularity conditions for exterior problems. Part 4 Numerical solution of potential flow problems: boundary integral equation formulation and numerical solution of selected problems. Part 5 Boundary integral equations for low Reynolds number flow: Greens' identities hydrodynamic single- and double-layer potentials indirect formulation Lyapunov-Tauber theorem for Stokes double-layer potential dynamic properties of the singularities and their distributions. Part 6 The low Reynolds number deformation of viscous drops and gas bubbles: viscous drop deformation compound drop deformation gas bubble deformation. Part 7 Navier-Stokes equations: velocity-pressure formulation velocity-vorticity formulation.