2,013 research outputs found
Advanced numerical methods for the simulation of alloy solidification with high Lewis number
A fully-implicit numerical method based upon adaptively refined meshes for the thermal-solutal simulation of alloy solidification in 2D is presented. In addition we combine an unconditional stable second-order fully-implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method, where a robust and fast multigrid solver for systems of non-linear algebraic equations is used to solve the intermediate approximations per time step. For the isothermal case, the superiority of this method, compared to widely used fully-explicit methods, with respect to CPU time and accuracy, has been demonstrated and published previously. Here, the new proposed method has been applied to the thermalsolutal case with high Lewis number, where stability issues and time step restrictions have been major constraints in previous research
Advanced numerical methods for mantle convection models
Numerical modelling of Earth's mantle is a complex, and computationally demanding task due to, amongst others, the broad spectrum of temporal and spatial scales playing a role in mantle flow, large uncertainties in the physical properties of mantle material, with large and localised transitions in viscosity and density. This thesis introduces and analyses a number of numerical techniques that may bring a significant contribution in meeting some of these challenges. Firstly, we introduce a novel time integration scheme for free surface movement in mantle convection models that is more accurate and stable for large time steps. Secondly, we extend the capabilities of anisotropic mesh optimisation, which allows efficient focussing of mesh resolution, to handle cylindrical and spherical shell domains and demonstrate that a significant reduction in the required number of degrees of freedom is possible while maintaing accuracy. Finally, to verify correctness, and evaluate and compare properties of various numerical schemes, we derive an extensive suite of analytical solutions to the Stokes equations governing mantle flow in cylindrical and spherical shell domains, with physically relevant boundary conditions. As a numerical benchmark they also serve to facilitate comparisons of different geodynamical models, and the further development of numerical techniques to improve these.Open Acces
ADVANCED NUMERICAL METHODS FOR THE DYNAMIC OPTIMISATION OF MECHANICAL COMPONENTS
This PhD thesis concerns the development and assessment
of innovative methodologies for simulating and improving the
dynamic behaviour of mechanical components. In particular, two
correlated issues are addressed herein: hybrid FE/LP gear pump
modelling as a tool for foreseeing and optimising vibration
behaviour in operational conditions; a new methodology for
vibration reduction by applying damping patches in appropriate
positions.
In the field of positive displacement pump modelling,
external gear pumps were analysed with the aim of developing
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advanced methodologies which accurately predict of the dynamic
behaviour of these components. Indeed, the first part of this thesis
(PART A) is about external gear pumps for steering systems; the
research activity concerning gear pumps was carried out in
collaboration with the Dept. of Engineering at the University of
Ferrara in co-operation with TRW Automotive Italia S.p.A â
Divisione Automotive Pumps (Ostellato, Ferrara, Italy). This
research pertains to the creation of a hybrid model, obtained
through the integration of a nonlinear elastodynamic model with
lumped parameters in relation to moving bodies, and an FE pump
model. The model referred to bodies in motion takes into account
the most important phenomena involved in pump operations,
such as time-varying oil pressure distribution on gears, timevarying
meshing stiffness, tooth profile errors, the possibility of
tooth contact, bush displacement and hydrodynamic journal
bearing reactions. Coupling the FE with the various parts which
make up the pump, as well as coupling the lumped-parameter
model and the FE model required the development of specific
advanced techniques; thus several problems related to the
combination of the different models employed in order to form a
single hybrid LP/FE model were studied and resolved. Using
particular techniques based on comparisons between simulations
and experimental results concerning acceleration, forces and
moments, the model was experimentally validated.
Although this hybrid model is an excellent tool for improving
the dynamic behaviour of gear pumps and for optimising the early
stages of prototype design, some problems can still remain related
to unwanted vibrations into precise frequency ranges. Thus, once
the first part of the research was completed, it was decided to
delve into the problem of structural optimisation. In particular, a
methodology for surface damping treatment was created and
applied. Indeed, the second part of the research activity (PART B)
was about the optimisation of mechanical components and
systems through the application of high damping material
components known as patches; this research activity is being
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carried out by the Dept. of Mechanical Engineering (laboratoire
vibrations acoustique) at the INSA institute (Institute National
des Sciences Appliquées) in Lyon (France) where I spent thirteen
months between the second and third year of my doctoral studies.
Such treatment can be applied to existing structures and provides
high damping capability over wide temperature and frequency
ranges. In many practical plate and machinery casing structures,
it is difficult to treat the whole surface with constrained layer
viscoelastic material, due to reduced areas or inaccessible parts.
Furthermore, it may indeed be desirable to selectively apply one
or more damping patches to control certain resonances. Patch
damping design is an efficient and cost effective concept for
solving noise and vibration problems. As a result of these
considerations, the research was focused on finding a general
methodology, based on a purely energetic approach, to reduce the
unwanted amplitude vibration level in mechanical components
through the application of appropriate elements characterized by
high damping properties. The methodology was enforced using IDEAS
v7! software which makes it possible to address modelling
in terms of energy distribution within a structure. Advanced
methodologies were developed to reduce the vibration amplitude
in components such as plate and bracket by applying patches.
Specifically, potential energy estimations will precisely and
accurately define the exact locations on the surface of the
components which should be covered by the patches. As a result,
these studies enable a reduction in vibration amplitude, in
reference both to a single component and/or a complex system. In
addition, this methodology makes it possible to improve the
vibratory behaviour of a component in certain frequency ranges
while reducing, at the same time, the effect of dangerous
resonances, acting specifically on the location, extent and
quantity of the patches to be applied on the surface of the base
component.
During this thesis, different fields were contemporarily
studied: definition and identification of structural modification
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methods, theoretical aspects of material damping characteristics,
vibrational propagation methods and applicative aspects relating
to the implementation of models for the vibratory optimisation of
mechanical components.
This thesis was developed within the LVA research and
technology transfer laboratories at the INSA institute (Lyon,
France) and InterMech (Division Acoustic and Vibrations â LAV);
and was carried out with the contribution of the Emilia Romagna
Region â Assessorato AttivitĂ Produttive, Sviluppo Economico,
Piano telematico, PRRIITT misura 3.4 azione A
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Global convection in Earth's mantle : advanced numerical methods and extreme-scale simulations
The thermal convection of rock in Earth's mantle and associated plate tectonics are modeled by nonlinear incompressible Stokes and energy equations. This dissertation focuses on the development of advanced, scalable linear and nonlinear solvers for numerical simulations of realistic instantaneous mantle flow, where we must overcome several computational challenges. The most notable challenges are the severe nonlinearity, heterogeneity, and anisotropy due to the mantle's rheology as well as a wide range of spatial scales and highly localized features. Resolving the crucial small scale features efficiently necessitates adaptive methods, while computational results greatly benefit from a high accuracy per degree of freedom and local mass conservation. Consequently, the discretization of Earth's mantle is carried out by high-order finite elements on aggressively adaptively refined hexahedral meshes with a continuous, nodal velocity approximation and a discontinuous, modal pressure approximation. These velocity--pressure pairings yield optimal asymptotic convergence rates of the finite element approximation to the infinite-dimensional solution with decreasing mesh element size, are inf-sup stable on general, non-conforming hexahedral meshes with "hanging nodes,'' and have the advantage of preserving mass locally at the element level due to the discontinuous pressure. However, because of the difficulties cited above and the desired accuracy, the large implicit systems to be solved are extremely poorly conditioned and sophisticated linear and nonlinear solvers including powerful preconditioning techniques are required. The nonlinear Stokes system is solved using a grid continuation, inexact Newton--Krylov method. We measure the residual of the momentum equation in the Hâ»Âč-norm for backtracking line search to avoid overly conservative update steps that are significantly reduced from one. The Newton linearization is augmented by a perturbation of a highly nonlinear term in mantle's rheology, resulting in dramatically improved nonlinear convergence. We present a new Schur complement-based Stokes preconditioner, weighted BFBT, that exhibits robust fast convergence for Stokes problems with smooth but highly varying (up to 10 orders of magnitude) viscosities, optimal algorithmic scalability with respect to mesh refinement, and only a mild dependence on the polynomial order of high-order finite element discretizations. In addition, we derive theoretical eigenvalue bounds to prove spectral equivalence of our inverse Schur complement approximation. Finally, we present a parallel hybrid spectral--geometric--algebraic multigrid (HMG) to approximate the inverses of the Stokes system's viscous block and variable-coefficient pressure Poisson operators within weighted BFBT. Building on the parallel scalability of HMG, our Stokes solver demonstrates excellent parallel scalability to 1.6 million CPU cores without sacrificing algorithmic optimality.Computational Science, Engineering, and Mathematic
Multiscale entanglement in ring polymers under spherical confinement
The interplay of geometrical and topological entanglement in semiflexible
knotted polymer rings confined inside a spherical cavity is investigated using
advanced numerical methods. By using stringent and robust algorithms for
locating knots, we characterize how the knot length lk depends on the ring
contour length, Lc and the radius of the confining sphere, Rc . In the no- and
strong- confinement cases we observe weak knot localization and complete knot
delocalization, respectively. We show that the complex interplay of lk, Lc and
Rc that seamlessly bridges these two limits can be encompassed by a simple
scaling argument based on deflection theory. The same argument is used to
rationalize the multiscale character of the entanglement that emerges with
increasing confinement.Comment: 9 pages 9 figure
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