A free element scheme for simulating two‐ and three‐dimensional incompressible fluid flow

Abstract

AbstractIn this work, Free Element method (FECM) is extended to solve incompressible Navier‐Stokes equations. The momentum equations are discretized by FECM, which permits overlapped elements. Then, the velocities at midpoints are interpolated by improved Momentum Interpolation Method to avoid oscillation caused by decoupling of velocity and pressure. At last, the pressure correction equation is solved to make sure the results satisfying continuity equation. The interpolation of midpoint's velocity is proved to be independent of the under‐relaxation factor and time step size. The deferred correction is employed for utilization of higher‐order discretization of convective terms. Taylor‐Green vortex, flow over a cylinder, lid‐driven flow, cooling tunnel, and flow over airfoil are simulated. The results computed by the proposed method are compared with exact solutions and benchmark solutions, which indicates that the new method has the second order accuracy in space. What is more, the proposed method works well on random node distributions as well, which means that the method is much robust.