Application of the parallel diagonal dominant algorithm for the incompressible Navier-Stokes equations

•Proved the applicability of the PDD algorithm for the incompressible Navier-Stokes equations.•Proved errors from the PDD algorithm are bounded regardless of diagonal dominance of tridiagonal matrices.•Investigated effects of the CFL number and the number of grid points on the accuracy.•Developed a highly scalable ADI-PDD method by utilizing an aggregative data communication method. The accuracy and the applicability of the parallel diagonal dominant (PDD) algorithm are explored for highly scalable computation of the incompressible Navier-Stokes equations which are integrated using a fully-implicit fractional-step method in parallel computational environments. The PDD algorithm is known to be applicable only for an evenly diagonal dominant matrix. In the present study, however, it is shown mathematically that the PDD algorithm is utilizable even for non-diagonal dominant matrices derived from discretization of incompressible momentum equations. The order of accuracy and the error characteristics are investigated in detail in terms of the Courant-Friedrichs-Lewy (CFL) number and the grid spacing by conducting simulations of decaying vortices in both two and three dimensions, flow in a lid-driven cavity, and flow over a circular cylinder. In order to reduce communication cost, which is one of bottlenecks in parallel computation, an aggregative data communication method is combined with the PDD algorithm. Parallel performance of the present PDD-based method is investigated by measuring the speedup, efficiency, overhead, and serial fraction.