A second order scheme for the Navier–Stokes equations: Application to the driven-cavity problem Original Research Article

In Guo, 1999, we investigated the stability and convergence of a second-order numerical scheme for computing two- and three-dimensional, time-dependent incompressible flows governed by the Navier–Stokes equations. In this article, we continue to discuss this scheme and we will focus on the applications. This scheme is based on the full discretization and matrix approximation. No supplementary boundary conditions on the velocity field and the pressure are needed. Numerical solutions for flows inside a driven cavity are presented and compared with other numerical results. We clearly observe the eddy motion for the driven cavity problem for the considered Reynolds numbers.