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...

Machine learning for the prediction of the local skin friction factors and Nusselt numbers in turbulent flows past rough surfaces

Turbulent flows past rough surfaces can create substantial energy losses in engineering equipment. During the last decades, developing accurate correlations to predict the thermal and hydrodynamic behavior of rough surfaces has proven to be a difficult challenge. In this work, we investigate the applicability of convolutional neural networks...

A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities

Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard (NSCH) models with non-matching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. The overarching objective of this work is to bring all of these models together by laying down...

A monolithic finite element formulation for the hydroelastic analysis of very large floating structures

In this work we present a novel monolithic Finite Element method for the hydroelastic analysis of very large floating structures (VLFS) with arbitrary shapes that is stable, energy conserving, and overcomes the need of an iterative algorithm. The new formulation enables a fully monolithic solution of the linear free-surface flow, described by...

Low-aspect ratio appendages for wind-assisted ships

Wind propulsion for commercial ships has been identified as a key component in the energy transition for the maritime industry. The sailing hybrid ship will operate with leeway (drift) angles to produce a lateral force known as sideforce, for steady operation under sail. In this paper, experimental results for the sailing performance of ships...

A novel diffuse-interface model and a fully-discrete maximum-principle-preserving energy-stable method for two-phase flow with surface tension and non-matching densities

Two well-established classes of the interface capturing models are the level-set and phase-field models. Level-set formulations satisfy the maximum principle for the density but are not energy-stable. On the other hand, phase-field models do satisfy the second law of thermodynamics but lack the maximum principle for the density. In this paper...

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...

MFEM: A modular finite element methods library

MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM's goal is to provide...

Isogeometric analysis of linear free-surface potential flow

This paper presents a novel variational formulation to simulate linear free-surface flow. The variational formulation is suitable for higher-order finite elements and higher-order and higher-continuity shape functions as employed in Isogeometric Analysis (IGA). The novel formulation combines the interior and free-surface problems in one...

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...

Toward free-surface flow simulations with correct energy evolution: An isogeometric level-set approach with monolithic time-integration

This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy behavior here means that the actual energy evolution of the numerical solution matches the evolution as...

Variation entropy: a continuous local generalization of the TVD property using entropy principles

This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation entropies. This provides insight into the total variation diminishing property and justifies it from...

Isogeometric modeling and experimental investigation of moving-domain bridge aerodynamics

Computational fluid dynamics (CFD) and fluid–structure interaction (FSI) are growing disciplines in the aeroelastic analysis and design of long-span bridges, which, with their bluff body characteristics, offer major challenges to efficient simulation. In this paper, we employ isogeometric analysis (IGA) based on nonuniform rational B-splines ...

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...

Monotone level-sets on arbitrary meshes without redistancing

In this paper we present a level-set approach that addresses two issues that can occur when the level-set approach is used to simulate two-fluid flows in engineering practice.<br/>The first issues is that of smoothing of the Heaviside on arbitrary meshes. It is shown that the Heaviside can be non-smooth on non-uniform meshes. Alternative...

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...