Also, A contains contributions from the linearization of the convective term, evaluated at some base velocity solution. For the SI method, the above method is also used, but produces a converged solution in one iteration, since the algebraic system is linear. Inner Iteration For the quasi-Newton scheme, Eq. The above iterative method is known as Richardson iteration, or residual correction. Note that the iterative scheme requires the inversion of M, rather than L, and that L is only needed as a multiplicative operator.
M differs from than the original system only in the momentum equation pressure coefficient.
The choice of M and the approximate factorization Eq. In the fractional step method, however, M replaces the original linear operator L, and the original linear system, Eq. In order to solve the first two steps of Eq. The velocity system is well-conditioned, and therefore converges rapidly with any reasonable iterative method. A preconditioned residual correction method as in Eq.