Finite element splitting methods applied to incompressible navier-stokes flow solvers and introduction to mixed mass method

Splitting Methods are considered to be a strong candidate for obtaining accurate, robust and computationally efficient incompressible Navier-Stokes (NS) solvers based on Finite Element Method. The type of spatial errors such as the numerical boundary layer observed on pressure solution near walls is known to affect the stability of NS solvers. The inclusion of stabilization terms such as upwinding or artificial viscosity terms would adversely affect the accuracy of the solver. NS solvers based on LBB compliant elements, such as Taylor Hood (TH) elements do not require stabilization terms to simulate higher Reynolds number flow provided their robustness is not affected by above mentioned type of error. This motivates the study of Splitting Methods based on Taylor Hood elements with the emphasis on how well they handle numerical boundary layer type errors to obtain highly accurate NS flow solvers. The effect of the enrichment of the TH elements with pressure bubble nodes is also investigated. The present work brings several well-known Splitting Methods under a common theoretical framework and classifies them appropriate to the study