Factorization methods for the numerical approximation of Navier-Stokes equations

We investigate a general approach for the numerical approximation of incompressible Navier–Stokes equations based on splitting the original problem into successive subproblems cheaper to solve. The splitting is obtained through 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 formal analogy with well known time advancing schemes, such as the projection Chorin–Temam's, can be pointed out. Features and limits of this analogy (that was earlier introduced in B. Perot, J. Comp. Phys. 108 (1993) 51–58) are addressed. Other, new methods can also be formulated starting from this approach: in particular, we introduce here the so called Yosida method, which can be investigated in the framework of quasi-compressibility schemes. Numerical results illustrating the different performances of the different methods here addressed are presented for a couple of test cases.