Explicit and implicit parallel solutions of 3-d Navier-Stokes equations on WS clusters

Second order accurate schemes, both in time and space, are implemented to solve complex flows. A modified version of the two step fractional method is used in time discretization of the momentum equation for both, the explicit and the implicit schemes. For the explicit scheme the momentum equation is solved twice and for the implicit scheme it is solved only once for each time step. In case of high Reynold number flows, a fourth order artificial viscosity is used to stabilize the solver. The pressure at each time level is obtained via solving the Poisson's equation satisfied by an auxiliary scalar potential. For the explicit scheme, however, grids having pQ2Q1 elements (coarse pressure field and fine velocity field resolution) are used to reduce the CPU time in solving Poisson's equation for pressure. Lid-driven cubic cavity flow is studied as the test case in demonstrating the accuracy and the robustness of the method. Up to half a million grid points are handled conviniently in accurate study of this complex flow case resolved with pQ2Q1 elements. In addition, as a more complex study, flow past a wing-winglet is solved with the explicit method.