Numerical study of the use of residual- and non-residual-based stabilized VMS formulations for incompressible power-law fluids

In this study, two stabilized, variational-multiscale-type finite element methods were assessed for the numerical approximation of incompressible fluids using anisotropic space–time discretizations. The first method has a classical residual structure, whereas the second has a non-residual term-by-term structure. In both cases, the computational benefits of using dynamic sub-scales are evaluated. A comparison between the two methods is made concerning (i) a numerical study of the influence of solvers (direct and iterative) in the approximation of power-law fluid flows using anisotropic space–time discretizations, (ii) their ability and performance to approximate dynamic and convective flows, and (iii) a sensitivity analysis of the formulations for the use of Lumped or L2 projections to define the orthogonal structure of the sub-scales. The problem employed to perform the numerical tests is the two-dimensional flow over an unconfined cylinder using Lagrangian P1 and P2 finite elements. The analyzed flows are characterized by Reynolds’ numbers 100 and 1,000 for power-law fluids. In addition, the study is extended to a three-dimensional problem using tetrahedral linear elements.