The Gauge–Uzawa methods for incompressible fluids with microstructure

Abstract

In this paper, the Gauge–Uzawa method for the time‐dependent incompressible micropolar fluid problem is proposed. Firstly, the first‐order and second‐order Euler semi‐implicit Gauge–Uzawa methods for the micropolar fluid are constructed, and the unconditionally stability analysis and error estimate of the corresponding first‐order scheme are deduced. Secondly, the fully discrete scheme with finite element approximation in space is presented, and the stability result of the corresponding first‐order scheme is derived. Finally, some numerical results are given, which test the theoretical analysis results.