Iterative methods for problems in computational fluid dynamics. (English) Zbl 0957.76071

Chan, Raymond H. (ed.) et al., Iterative methods in scientific computing. Papers from the winter school on Iterative methods in scientific computing and their applications held in Hong Kong, December 14-20, 1995. Singapore: Springer. 271-327 (1997).
Summary: We discuss iterative methods for solving algebraic systems of equations arising from linearization and discretization of primitive variable formulations of incompressible Navier-Stokes equations. Implicit discretization in time leads to a coupled but linear system of partial differential equations at each time step, and discretization in space then procedures a series of linear algebraic systems. We give an overview of commonly used time and space discretization techniques, and we discuss a variety of algorithmic strategies for solving the resulting systems of equations. The emphasis is on preconditioning techniques, which can be combined with Krylov subspace iterative methods. In many cases the solution of subsidiary problems such as the discrete convection-diffusion equation and the discrete Stokes equations plays a crucial role. We examine iterative techniques for these problems and show how they can be integrated into effective solution algorithms for the Navier-Stokes equations.
For the entire collection see [Zbl 0921.00025].


76M99 Basic methods in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65F10 Iterative numerical methods for linear systems
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics