Efficient and Unconditional Energy Stable Schemes for the Micropolar Navier-Stokes Equations

Abstract

We develop in this paper efficient numerical schemes for solving the micropolar Navier-Stokes equations by combining the SAV approach and pressure-correction method. Our firstand second-order semi-discrete schemes enjoy remarkable properties such as (i) unconditional energy stable with a modified energy, and (ii) only a sequence of decoupled linear equations with constant coefficients need to be solved at each time step. We also construct fully discrete versions of these schemes with a special spectral discretization which preserve the essential properties of the semi-discrete schemes. Numerical experiments are presented to validate the proposed schemes. AMS subject classifications: 65M12, 65M70, 35Q30, 76A05