A segregated implicit solution algorithm for 2D and 3D laminar incompressible flows.

*(English)*Zbl 0863.76051Summary: A segregated algorithm for the solution of laminar incompressible, two- and three-dimensional flow problems is presented. This algorithm employs the successive solution of the momentum and continuity equations by means of a decoupled implicit solution method. The inversion of the coefficient matrix which is common for all momentum equations is carried out through an approximate factorization in upper and lower triangular matrices. The divergence-free velocity constraint is satisfied by formulating and solving a pressure correction equation. For the latter, a combined application of a preconditioning technique and a Krylov subspace method is employed and proved to be more efficient than the approximate factorization method. The method exhibits a monotonic convergence, it is not costly in CPU time per iteration and provides accurate solutions which are independent of the underrelaxation parameter used in the momentum equations. Results are presented on two- and three-dimensional flow problems.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

##### Keywords:

approximate factorization; triangular matrices; divergence-free velocity constraint; pressure correction equation; preconditioning technique; Krylov subspace method; monotonic convergence; finite volume method
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\textit{K. C. Giannakoglou} and \textit{E. S. Politis}, Int. J. Numer. Methods Fluids 21, No. 11, 1067--1086 (1995; Zbl 0863.76051)

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