Finite element solution of three‐dimensional incompressible fluid flow problems by a preconditioned conjugate residual method

A new algorithm for the solution of the three‐dimensional Navier–Stokes equation using the mixed formulation and an incomplete factorization technique is presented. The linear system obtained at each modified Newton–Raphson iteration is solved by the preconditioned conjugate residual method (PCR) using an out‐of‐core incomplete LU factorization as preconditioning. This factorization is performed on a matrix stored by a new static storage method called the packed skyline method. The performance of the proposed algorithm is assessed for the wall‐driven cubic cavity problem using the Q − P 1 enriched element.