Analysis of a Novel Time Filter Algorithm for the Time‐Dependent Incompressible Thermomicropolar Fluid Equations

In this paper, we present an efficient numerical algorithm for solving time‐dependent thermomicropolar fluid equations. The proposed method combines a first‐order ‐scheme, based on the linear multi‐step method (LM), with a time filter (TF) (referred to as LMTF). This approach enhances the temporal convergence rate from first‐order to second‐order accuracy while preserving computational efficiency and implementation simplicity. The algorithm first computes the linear velocity and pressure, then solves for the angular velocity, and finally for temperature, effectively decoupling the entire system. We provide a rigorous theoretical analysis of the decoupled LMTF scheme, proving its stability and deriving error estimates. Numerical experiments confirm the algorithm's effectiveness.