A class of fully second order accurate projection methods for solving the incompressible Navier–Stokes equations

Abstract

In this paper, a continuous projection method is designed and analyzed. The continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the Navier–Stokes (N–S) equations in each time interval of a given time discretization. The local truncation error (LTE) analysis is applied to the continuous projection methods, which yields a sufficient condition for the continuous projection methods to be temporally second order accurate. Based on this sufficient condition, a fully second order accurate discrete projection method is proposed. A heuristic stability analysis is performed to this projection method showing that the present projection method can be stable. The stability of the present scheme is further verified through numerical experiments. The second order accuracy of the present projection method is confirmed by several numerical test cases.