Handbook of Numerical Analysis. Numerical Methods for Fluids

Roland Glowinski, Jacques Louis Lions, P. G. Ciarlet, Jacques Louis Lions, Philippe G. Ciarlet0444512241, 9780444512246, 9780080507941

Hardbound. This book size article is dedicated to the numerical simulation of unsteady incompressible viscous flow modelled by the Navier – Stokes equations, or by non-Newtonian variants of them. In order to achieve this goal we have developed a methodology based on the following tools:
(i) Time discretization by operator splitting schemes such as Peaceman – Rachford’s, Douglas – Rachford’s ,Marchuk – Yanenko’s, Strang’s symmetrized, and the so-called theta – scheme introduced by the author in the mid – eighties.
(ii) Projection methods (in L2 or H1) for the treatment of the incompressibility condition div u = 0.
(iii) Treatment of the advection by: either a centered scheme leading to linear or nonlinear advection – diffusion problems solved by least squares / conjugate gradient algorithms, or to a linear wave – like equation well suited to finite element based solution methods.