Construction and application of an algebraic dual basis and the Fine-Scale Greens’ Function for computing projections and reconstructing unresolved scales

In this paper, we build on the work of Hughes and Sangalli (2007) dealing with the explicit computation of the Fine-Scale Greens’ function. The original approach chooses a set of functionals associated with a projector to compute the Fine-Scale Greens’ function. The construction of these functionals, however, does not generalise to arbitrary...

Nitsche's method as a variational multiscale formulation and a resulting boundary layer fine-scale model

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms of Nitsche's method all originate from the fine-scale closure dictated by the corresponding scale...

A theoretical framework for discontinuity capturing: Joining variational multiscale analysis and variation entropy theory

In this paper we show that the variational multiscale method together with the variation entropy concept form the underlying theoretical framework of discontinuity capturing. The variation entropy [M.F.P. ten Eikelder and I. Akkerman, Comput. Methods Appl. Mech. Engrg. 355 (2019) 261-283] is the recently introduced concept that equips total...

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

This paper presents the construction of novel stabilized finite element methods in the convective–diffusive context that exhibit correct-energy behavior. Classical stabilized formulations can create unwanted artificial energy. Our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small...

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

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...

Adaptive Variational Multiscale Formulations using the Discrete Germano

A Residual-Based Large-Eddy Simulation (RB-LES) method is developed. This is done by discretizing the Navier-Stokes equations directly. A priori filtering is omitted. Analytical approximation of the subgrid scales results in a unusually-stabilized finite-element method with additional terms arising due to the nonlinearity. This RB-LES method is...

The role of continuity in residual-based variational multiscale modeling of turbulence

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135–4195, 2005). We make use of quadratic discretizations...

Preliminary investigation of overlap coupling for hybrid LES/RANS