Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier–Stokes equations

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier–Stokes equations

ten Eikelder, M.F.P. (TU Delft Ship Hydromechanics and Structures)
Akkerman, I. (TU Delft Ship Hydromechanics and Structures)

2018

This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier–Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective–diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259–280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection–diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov–Galerkin (SUPG) and the Galerkin/least-squares method (GLS). The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large- and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.

Energy decay
Incompressible flow
Isogeometric analysis
Orthogonal small-scales
Residual-based variational multiscale method
Stabilized methods

http://resolver.tudelft.nl/uuid:d031111a-5862-49ac-98ac-c9553574fc2f

https://doi.org/10.1016/j.cma.2018.02.030

2020-03-07

0045-7825

Computer Methods in Applied Mechanics and Engineering, 340, 1135-1154

Accepted Author Manuscript

Institutional Repository

journal article

© 2018 M.F.P. ten Eikelder, I. Akkerman