Factorization methods for the numerical approximation of Navier-Stokes equations

We investigate a general approach for the numerical approximation of incomp ressible Navier-Stokes equations based on splitting the original problem in to successive subproblems cheaper to solve. The splitting is obtained throu gh an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations. Several schemes based on approximate factorization are investigated, For some of these methods a fo rmal analogy with well known time advancing schemes, such as the projection Chorin-Temam's, can be pointed out. Features and limits of this analogy (t hat was earlier introduced in B. Perot, J. Comp. Phys. 108 (1993) 51-58) ar e addressed. Other, new methods can also be formulated starting from this a pproach: in particular, we introduce here the so called Yosida method, whic h can be investigated in the framework of quasi-compressibility schemes. Nu merical results illustrating the different performances of the different me thods here addressed are presented for a couple of test cases. (C) 2000 Els evier Science S.A. All rights reserved.