A second order time filter backward Euler algorithm for the time‐dependent incompressible thermomicropolar fluid equations

Abstract This article constructs a decoupled time filter (TF) algorithm for the time‐dependent incompressible thermomicropolar fluid equations. The proposed method is divided into two steps. In the first step, the numerical solutions of velocity and pressure, angular velocity, and temperature are calculated successively. A TF step is added as the second step, which improve the temporal accuracy (i.e., to , or to ), without a significant increase in computational complexity. The unconditional stability and second‐order temporal convergence for the proposed algorithm are presented. Furthermore, some 2D/3D numerical experiments are provided to validate the theoretical results. Additionally, the proposed method is applied to the backward differentiation formula of second‐order scheme and achieves third‐order temporal convergence in 2D and 3D numerical experiments.