In this work, we present numerical comparisons of some stabilization methods for the incompressible Navier–Stokes. The first is the characteristic‐based split (CBS). It combines the characteristic Galerkin method to deal with convection‐dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity–pressure interpolations. The other two approaches are particular cases of the subgrid scale (SGS) method. The first, obtained after an algebraic approximation of the subgrid scales, is very similar to the popular Galerkin/least‐squares (GLS) method, whereas in the second, the subscales are assumed to be orthogonal to the finite element space. It is shown that all these formulations display similar stabilization mechanisms, provided the stabilization parameter of the SGS methods is identified with the time step of the CBS approach. This paper provides the numerical experiments for the comparison of formulations made by Codina and Zienkiewicz in a previous article.

Q. Wang, S. Danilov, J. Schröter. Finite element ocean circulation model based on triangular prismatic elements, with application in studying the effect of topography representation. J. Geophys. Res. 113(C5) (2008) DOI 10.1029/2007jc004482

A. Limache, S. Idelsohn, R. Rossi, E. Oñate. The violation of objectivity in Laplace formulations of the Navier–Stokes equations. Int. J. Numer. Meth. Fluids 54(6-8) (2007) DOI 10.1002/fld.1480

C. Thomas, P. Nithiarasu, R. Bevan. The locally conservative Galerkin (LCG) method for solving the incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids 57(12) DOI 10.1002/fld.1683

P. Nithiarasu, O. Hassan, K. Morgan, N. Weatherill, C. Fielder, H. Whittet, P. Ebden, K. Lewis. Steady flow through a realistic human upper airway geometry. Int. J. Numer. Meth. Fluids 57(5) (2008) DOI 10.1002/fld.1805

S. Singh, P. Nithiarasu, P. Eng, R. Lewis, A. Arnold. An implicit–explicit solution method for electro-osmotic flow through three-dimensional micro-channels. Int. J. Numer. Meth. Engng 73(8) (2008) DOI 10.1002/nme.2104

H. Lee, K. Kim, J. Kim. On the long time simulation of the Rayleigh-Taylor instability. Int. J. Numer. Meth. Engng. 85(13) (2010) DOI 10.1002/nme.3034

P. Nithiarasu. A unified fractional step method for compressible and incompressible flows, heat transfer and incompressible solid mechanics. Int Jnl of Num Meth for HFF 18(2) DOI 10.1108/09615530810846284

A. NICOLLE, I. EAMES. Numerical study of flow through and around a circular array of cylinders. J. Fluid Mech. 679 (2011) DOI 10.1017/jfm.2011.77

J. Mynard, P. Nithiarasu. A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method. Commun. Numer. Meth. Engng. 24(5) (2008) DOI 10.1002/cnm.1117

K. Chitra, S. Vengadesan, T. Sundararajan, P. Nithiarasu. An investigation of pulsatile flow in a model cavo-pulmonary vascular system. Commun. Numer. Meth. Engng. 25(11) DOI 10.1002/cnm.1205

P. Nithiarasu, I. Sazonov, S. Yeo. Scan-Based Flow Modelling in Human Upper Airways. (2011) DOI 10.1007/8415_2011_100

R. Bevan, P. Nithiarasu. A dual time stepping approach to eliminate first order error in fractional step methods for incompressible flows. Int Jnl of Num Meth for HFF 26(2) DOI 10.1108/hff-03-2015-0090

R. Bevan, E. Boileau, R. van Loon, R. Lewis, P. Nithiarasu. A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows. Int Jnl of Num Meth for HFF 26(3/4) DOI 10.1108/hff-06-2015-0233

E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suárez. Possibilities of the particle finite element method for fluid–soil–structure interaction problems. Comput Mech 48(3) (2011) DOI 10.1007/s00466-011-0617-2

E. Oñate, J. Carbonell. Updated lagrangian mixed finite element formulation for quasi and fully incompressible fluids. Comput Mech 54(6) (2014) DOI 10.1007/s00466-014-1078-1