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.