Modeling incompressible flows at low and high Reynolds numbers via a finite calculus–finite element approach

We present a formulation for incompressible flows analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus (FIC) method. The stabilization terms introduced by the FIC formulation allow to solve a wide range of fluid flow problems for low and high Reynolds numbers flows without the need for a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows with moderate and large Reynolds numbers are presented

A FIC-based stabilized finite element formulation for turbulent flows

We present a new stabilized finite element (FEM) formulation for incompressible flows based on the Finite Increment Calculus (FIC) framework. In comparison to existing FIC approaches for fluids, this formulation involves a new term in the momentum equation, which introduces non-isotropic dissipation in the direction of velocity gradients. We also follow a new approach to the derivation of the stabilized mass equation, inspired by recent developments for quasi-incompressible flows. The presented FIC-FEM formulation is used to simulate turbulent flows, using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation.Peer ReviewedPostprint (author's final draft

Computation of turbulent flows using a finite calculus–finite element formulation

We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented

Computational of turbulent flows using a finite element formulation

We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.Preprin

Computation of turbulent flows using a finite element formulation

We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented

Finite increment calculus (FIC). A framework for deriving enhanced computational methods in mechanics

In this paper we present an overview of the possibilities of the finite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diffusion-reaction, fluid mechanics and fluid-structure interaction solved with the finite element method (FEM). Examples of the good features of the FIC/FEM technique for solving some of these problems are given. A brief outline of the possibilities of the FIC/FEM approach for error estimation and mesh adaptivity is given

Stationary shapes of deformable particles moving at low Reynolds numbers

Lecture Notes of the Summer School ``Microswimmers -- From Single Particle Motion to Collective Behaviour'', organised by the DFG Priority Programme SPP 1726 (Forschungszentrum J{\"{u}}lich, 2015).Comment: Pages C7.1-16 of G. Gompper et al. (ed.), Microswimmers - From Single Particle Motion to Collective Behaviour, Lecture Notes of the DFG SPP 1726 Summer School 2015, Forschungszentrum J\"ulich GmbH, Schriften des Forschungszentrums J\"ulich, Reihe Key Technologies, Vol 110, ISBN 978-3-95806-083-

LES turbulence models. Relation with stabilized numerical methods

One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. A relevant aspect of LES theory, which we will consider in our work, is the close relationship between the mathematical properties of LES models and the numerical methods used for their implementation. In last years it is more and more common the idea in the scientific community, especially in the numerical community, that turbulence models and stabilization techniques play a very similar role. Methodologies used to simulate turbulent flows, RANS or LES approaches, are based on the same concept: unability to simulate a turbulent flow using a finite discretization in time and space. Turbulence models introduce additional information (impossible to be captured by the approximation technique used in the simulation) to obtain physically coherent solutions. On the other side, numerical methods used for the integration of partial differential equations (PDE) need to be modified in order to able to reproduce solutions that present very high localized gradients. These modifications, known as stabilization techniques, make possible to capture these sharp and localized changes of the solution. According with previous paragraphs, the following natural question appears: Is it possible to reinterpret stabilization methods as turbulence models? This question suggests a possible principle of duality between turbulence modelling and numerical stabilization. More than to share certain properties, actually, it is suggested that the numerical stabilization can be understood as turbulence. The opposite will occur if turbulence models are only necessary due to discretization limitations instead of a need for reproducing the physical behaviour of the flow. Finally: can turbulence models be understood as a component of a general stabilization method