Iterative Methods for Problems in Computational Fluid Dynamics
Publication or External Link
We discuss iterative methods for solving the algebraic systems of equations
arising from linearization and discretization of primitive variable
formulations of the 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 produces 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. (Also cross-referenced as UMIACS-TR-96-58)