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 approxima-tion 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 L-2 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 P-1 and P-2 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. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this study, two stabilized variational-multiscale-type finite element methods were assessed for the numerical approximation of incompressible fluids. The performance of these methods was compared under different conditions, and some influencing factors were investigated. The experimental results indicate that these two methods have different ranges of applicability and effectiveness.