Pressure correction algebraic splitting methods for the incompressible Navier-Stokes equations

摘要

In this paper we present a new family of methods for the effective numerical solution of the incompressible unsteady Navier-Stokes equations. These methods resort to an algebraic splitting of the discretized problem based on inexact LU block factorizations of the corresponding matrix (following [A. Quarteroni, F. Saleri, and A. Veneziani, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505-526]. In particular, we will start from inexact algebraic factorizations of algebraic Chorin-Temam and Yosida type and introduce a pressure correction step aimed at improving the time accuracy. One of the schemes obtained in this way (the algebraic Chorin-Temam pressure correction method) resembles a method previously introduced in the framework of differential projection schemes (see [L. Timmermans, P. Minev, and F. V. de Vosse, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 673-688], [A. Prohl, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations, Teubner, Stuttgart, 1997]. The stability and the dependence of splitting error on the time step of the new methods is investigated and tested on several numerical cases.