Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier-Stokes equations

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