• The basic equation of fluid dynamics.- Partial differential equations: analytic aspects.- Finite volume and finite difference discretization on nonuniform grids.- The stationary convection-diffusion equation.- The nonstationary convection-diffusion equation.- The incompressible Navier-Stokes equations.- Iterative methods.- The shallow-water equations.- Scalar conservation laws.- The Euler equations in one space dimension.- Discretization in general domains.- Numerical solution of the Euler equations in general domains.- Numerical solution of the Navier-Stokes equations in general domains.- Unified methods for computing incompressible and compressible flow.

"This book is a well-written graduate level text in computational fluid dynamics. The text begins with a rather thorough discussion and derivation of the equations of fluid dynamics, followed by a review of topics in the theory of partial differential equations. There is a good introduction to the two numerical methods, finite volume and finite difference, that are treated in this text. The material is well-organized, starting with simple one-dimensional equations and moving to numerical methods for two-dimensional and three-dimensional problems. Grids are treated in some detail. In addition to simple colocated grids, there is discussion of non-uniform, staggered, and unstructured grids. There is a good mixture of theoretical and computational topics. This text should be of value to all researchers interested in computational fluid dynamics." -- MATHEMATICAL REVIEWS