Numerical solution of the incompressible Navier-Stokes equations. (English) Zbl 0784.76020

Quartapelle, Luigi

ISNM. International Series of Numerical Mathematics. 113. Basel: Birkäuser. xii, 291 p. (1993).

Methods for the approximate solution of the incompressible Navier-Stokes equations are investigated. Several numerical schemes are developed for the calculation of both steady and unsteady viscous flow using the various possible formulations of the equations. Both velocity-pressure and vorticity-streamfunction formulations in two and three dimensions are considered. An important aspect of the numerical methods is the proper specification of the boundary conditions. Further the attention is focused on time-dependent equations in which the incompressibility condition is imposed by means of a Poisson equation for a scalar or vector unknown. Also uncoupled versions of the equations are investigated.

Reviewer: W.Heinrichs (Düsseldorf)

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Mxx	Basic methods in fluid mechanics

Keywords:

velocity-pressure formulation; vorticity-streamfunction formulation; incompressibility condition; Poisson equation