Research on three kinds of splitting finite element schemes for 2D/3D unsteady incompressible thermomicropolar fluid equations

Abstract

In this article, three kinds of splitting finite element schemes are proposed for the 2D/3D unsteady incompressible thermomicropolar fluid equations, which are named as the standard splitting scheme, the consistent splitting schemes (I and II) and the splitting Oseen scheme. The unconditionally energy stable of all the schemes and error estimation of the standard splitting scheme are proved. Furthermore, numerical experiments are carried out on the last two kinds of schemes based on different selection of finite element pairs, numerical resultsshow that the presented schemes are reliable, especially some not inf-sup stable finite element pairs can also be applied for the consistent splitting scheme II. In addition, for moderate Reynolds number problems, the splitting Oseen scheme exhibit the better performance of numerical stability than the consistent splitting schemes.