From multi- to single-grid CFD on massively parallel computers: Numerical experiments on lid-driven flow in a cube using pressure-velocity coupled formulation

A parallel implementation of a fully pressure-velocity coupled multigrid solver based on analytical solution accelerated coupled line Gauss Seidel (ASA-CLGS) smoother with grid partitioning is carried out. The parallelized algorithm is characterized by an enhanced scalability that results from a formulation enabling an intermediate analytical solution for the entire row (column) of control volumes. General strategies of applying single- or multigrid approach depending on flow characteristics are discussed. Performance of the parallelized algorithm is studied for up to 2048 processors. The developed approach is applied to analysis of a time-dependent three-dimensional incompressible lid-driven cavity flow. The steady state results of benchmark quality are reported for Re=10³, 1.5×10³ and 1.9×10³. A new benchmark case of a fully 3D flow in a cubic cavity driven by the lid moving at 45° relatively to its lateral boundaries is proposed and the corresponding data is reported.