The dissipative structure of variational multiscale methods for incompressible flows

In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented

Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models

This paper builds on a recently developed immersogeometric fluid–structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition, the paper presents a comparison between FSI analysis and standalone structural dynamics simulation driven by prescribed transvalvular pressure, the latter being a more common modeling choice for this class of problems. The FSI computation achieved better physiological realism in predicting the valve leaflet deformation than its standalone structural dynamics counterpart

Lagrangian FE methods for coupled problems in fluid mechanics

This work aims at developing formulations and algorithms where maximum advantage of using Lagrangian finite element fluid formulations can be taken. In particular we concentrate our attention at fluid-structure interaction and thermally coupled applications, most of which originate from practical “real-life” problems. Two fundamental options are investigated - coupling two Lagrangian formulations (e.g. Lagrangian fluid and Lagrangian structure) and coupling the Lagrangian and Eulerian fluid formulations. In the first part of this work the basic concepts of the Lagrangian fluids, the so-called Particle Finite Element Method (PFEM) [1], [2] are presented. These include nodal variable storage, mesh re-construction using Delaunay triangulation/tetrahedralization and alpha shape-based method for identification of the computational domain boundaries. This shall serve as a general basis for all the further developments of this work.Postprint (published version

Numerical methods for the modelling of chip formation

The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been significant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches.Postprint (author's final draft

Lagrangian FE methods for coupled problems in fluid mechanics

Lagrangian finite element methods emerged in fluid dynamics when the deficiencies of the Eulerian methods in treating free surface flows (or generally domains undergoing large shape deformations) were faced. Their advantage relies upon natural tracking of boundaries and interfaces, a feature particularly important for interaction problems. Another attractive feature is the absence of the convective term in the fluid momentum equations written in the Lagrangian framework resulting in a symmetric discrete system matrix, an important feature in case iterative solvers are utilized. Unfortunately, the lack of the control over the mesh distortions is a major drawback of Lagrangian methods. In order to overcome this, a Lagrangian method must be equipped with an efficient re-meshing tool. This work aims at developing formulations and algorithms where maximum advantage of using Lagrangian finite element fluid formulations can be taken. In particular we concentrate our attention at fluid-structure interaction and thermally coupled applications, most of which originate from practical “real-life” problems. Two fundamental options are investigated - coupling two Lagrangian formulations (e.g. Lagrangian fluid and Lagrangian structure) and coupling the Lagrangian and Eulerian fluid formulations. In the first part of this work the basic concepts of the Lagrangian fluids, the so-called Particle Finite Element Method (PFEM) [1], [2] are presented. These include nodal variable storage, mesh re-construction using Delaunay triangulation/tetrahedralization and alpha shape-based method for identification of the computational domain boundaries. This shall serve as a general basis for all the further developments of this work. Next we show how an incompressible Lagrangian fluid can be used in a partitioned fluid-structure interaction context. We present an improved Dirichlet-Neumann strategy for coupling the incompressible Lagrangian fluid with a rigid body. This is finally applied to an industrial problem dealing with the sea-landing of a satellite capsule. In the following, an extension of the method is proposed to allow dealing with fluid-structure problems involving general flexible structures. The method developed takes advantage of the symmetry of the discrete system matrix and by introducing a slight fluid compressibility allows to treat the fluid-structure interaction problem efficiently in a monolithic way. Thus, maximum benefit from using a similar description for both the fluid (updated Lagrangian) and the solid (total Lagrangian) is taken. We show next that the developed monolithic approach is particularly useful for modeling the interaction with light-weight structures. The validation of the method is done by means of comparison with experimental results and with a number of different methods found in literature. The second part of this work aims at coupling Lagrangian and Eulerian fluid formulations. The application area is the modeling of polymers under fire conditions. This kind of problem consists of modeling the two subsystems (namely the polymer and the surrounding air) and their thermomechanical interaction. A compressible fluid formulation based on the Eulerian description is used for modeling the air, whereas a Lagrangian description is used for the polymer. For the surrounding air we develop a model based upon the compressible Navier-Stokes equations. Such choice is dictated by the presence of high temperature gradients in the problem of interest, which precludes the utilization of the Boussinesq approximation. The formulation is restricted to the sub-sonic flow regime, meeting the requirement of the problem of interest. The mechanical interaction of the subsystems is modeled by means of a one-way coupling, where the polymer velocities are imposed on the interface elements of the Eulerian mesh in a weak way. Thermal interaction is treated by means of the energy equation solved on the Eulerian mesh, containing thermal properties of both the subsystems, namely air and polymer. The developments of the second part of this work do not pretend to be by any means exhaustive; for instance, radiation and chemical reaction phenomena are not considered. Rather we make the first step in the direction of modeling the complicated thermo-mechanical problem and provide a general framework that in the future can be enriched with a more detailed and sophisticated models. However this would affect only the individual modules, preserving the overall architecture of the solution procedure unchanged. Each chapter concludes with the example section that includes both the validation tests and/or applications to the real-life problems. The final chapter highlights the achievements of the work and defines the future lines of research that naturally evolve from the results of this work

Numerical Methods for the Modelling of Chip Formation

The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been significant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches

Analytical and Numerical Aspects of Porous Media Flow

The Brinkman equations model fluid flow through porous media and are particularly interesting in regimes where viscous shear effects cannot be neglected. Two model parameters in the momentum balance function as weights for the terms related to inter-particle friction and bulk resistance. If these are not in balance, then standard finite element methods might suffer from instabilities or error estimates might deteriorate. In particular the limit case, where the Brinkman problem reduces to a Darcy problem, demands for special attention. This thesis proposes a low-order finite element method which is uniformly stable with respect to the flow regimes captured by the Brinkman model, including the Darcy limit. To that end, linear equal-order approximations are combined with a pressure stabilization technique, a grad-div stabilization, and a penalty-free non-symmetric Nitsche method. The combination of these ingredients allows to develop a robust method, which is proven to be well-posed for the whole family of problems in two spatial dimensions, even if any Brinkman parameter vanishes. An a priori error analysis reveals optimal convergence in the considered norm. A convergence study based on problems with known analytic solutions confirms the robust first order convergence for reasonable ranges of numerical (stabilization) parameters. Further, numerical investigations that partly extend the theoretical framework are considered, revealing strengths and weaknesses of the approach. An application motivated by the optimization of geothermal energy production completes the thesis. Here, the proposed method is included in a multi-physics discrete model, appropriate to describe the thermo-hydraulics in hot, sedimentary, essentially horizontal aquifers. An immersed boundary method is adopted in order to allow a flexible, automatic optimization without regenerating the computational mesh. Utilizing the developed computational framework, the optimized multi-well arrangements with respect to the net energy gain are presented and discussed for different geothermal and hydrogeological setups. The results show that taking into account heterogeneous permeability structures and variable aquifer temperatures might drastically affect the optimal configuration of the wells