Pressure correction method with time filter for incompressible Navier–Stokes equations

Abstract

In this paper, we present standard pressure correction (SPC) and rotational pressure correction (RPC) methods with time filters for two- or three-dimensional (2D/3D) time-dependent incompressible Navier–Stokes equations. The core technique of these methods is to add a time filter at each time step after the original first- and second-order pressure correction methods, which not only decouples velocity and pressure, but also improves the temporal accuracy from first-order to second-order and from second-order to third-order, while not increasing additional computational complexity. Furthermore, combining the original pressure correction method, the pressure correction method plus time filter and the adaptive algorithm design idea, we constructed easy-to-implement adaptive time stepsize pressure correction algorithms and variable stepsize, variable order (VSVO) pressure correction algorithms. We also prove that both first-order SPC and RPC algorithms plus time filter are unconditionally stable and establish error estimates of the velocity for the first-order SPC method plus time filter. Finally, we provide numerical tests to demonstrate the performance of the proposed algorithm, with particular emphasis on the outstanding results achieved by the VSVO pressure correction method.