On pressure–velocity coupled time-integration of incompressible Navier–Stokes equations using direct inversion of Stokes operator or accelerated multigrid technique

Two fully pressure–velocity coupled approaches to time-integration of two- and three-dimensional Navier–Stokes equations discretized by finite volume method are proposed and verified. The first approach utilizes a direct sparse matrix solver to inverse the Stokes operator. In the second approach a multigrid iterative solver is accelerated by a modification of CLGS smoother that allows for derivation of an analytical solution for velocity and pressure corrections belonging to a whole row or column of finite volumes. Both approaches are tested by two- and three-dimensional natural convection benchmark problems. It is concluded that the analytical solution accelerated CLGS technique (ASA-CLGS) can be considered as a promising tool for solution of time-dependent three-dimensional fluid dynamics problems.