A modified characteristics projection finite element method for the micropolar Navier-Stokes equations

This paper presents a modified characteristics projection finite element method (MCPFEM) for solving the unsteady Micropolar Navier-Stokes Equations (MNSE). The proposed method integrates two key computational techniques: the modified characteristics finite element method, which linearizes nonlinear terms, and the pressure-correction projection method, which decouples velocity and pressure. This innovative integration yields an efficient numerical scheme, with only three independent linear systems needing solution at each time step. A rigorous theoretical framework for the MCPFEM is established, including proofs of its unconditional stability and derivations of optimal error estimates in both L 2 and H 1 norms. Comprehensive numerical simulations of velocity, pressure, and angular velocity fields demonstrate the method’s effectiveness. Our results show that the MCPFEM offers significant advantages in computational efficiency while maintaining accuracy in capturing the complex dynamics of micropolar fluids, confirming it as an accurate and computationally efficient framework for solving the MNSE system.