885 research outputs found
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New âdirectionalâ cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells
Une méthode mixte multi-échelles pour un simulateur de réservoir biphasé
A multiscale hybrid mixed finite element method is presented in this paper to solve two-phase flow equations on heterogeneous media under the effect of gravitational segregation. It is designed to cope with the complex geometry and inherent multiscale nature of the rocks, leading to stable and accurate multi-physics reservoir simulations. This multiscale approach makes use of coarse scale fluxes between subregions (macro domains) that allow to reduce substantially the dominant computational costs associated with the flux/pressure kernel embedded in the numerical model. As such, larger scale problems can be approximated in a reasonable computational time. Dividing the problems into macro domains leads to a hierarchy of meshes and approximation spaces, allowing the efficient use of static condensation and parallel computation strategies. The method documented in this work utilizes discretizations based on a general domain partition formed by poly-hedral subregions. The normal flux between these subregions is associated with a finite dimensional trace space. The global system to be solved for the fluxes and pressures is expressed only in terms of the trace variables and of a piecewise constant pressure associated with each subregion. The fine scale features are resolved by mixed finite element approximations using fine flux and pressure representations inside each subregion, and the trace variable (i.e. normal flux) as Neumann boundary conditions. This property implies that the flux approximation is globally H(div)-conforming, and, as in classical mixed formulations, local mass conservation is observed at the micro-scale elements inside the subregions, an essential property for flows in heterogeneous media
Semiannual report
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period 1 Oct. 1994 - 31 Mar. 1995
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Office of Advanced Scientific Computing Research Applied Mathematics Principal Program Annual PI Meeting Abstracts
Das unstetige Galerkinverfahren fĂŒr Strömungen mit freier OberflĂ€che und im Grundwasserbereich in geophysikalischen Anwendungen
Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory.
Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing.
This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.FĂŒr viele geophysikalische Anwendungen spielen Strömungen mit freier OberflĂ€che und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch fĂŒr diese Anwendungsszenarien sind groĂe Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit betrĂ€chtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten.
Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an FlexibilitĂ€t und sind fĂŒr paralleles Rechnen gut geeignet.
Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher fĂŒr Strömungen mit freier OberflĂ€che und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete StabilitĂ€tsanalyse des gekoppelten Modells
A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations
In this work we propose a novel block preconditioner, labelled Explicit
Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov
subspace solvers used to address the sequence of non-symmetric systems of
linear equations originating from flow simulations in porous media. The flow
model is discretized blending the Mixed Hybrid Finite Element (MHFE) method for
Darcy's equation with the Finite Volume (FV) scheme for the mass conservation.
The EDFA preconditioner is characterized by two features: the exploitation of
the system matrix decoupling factors to recast the Schur complement and their
inexact fully-parallel computation by means of restriction operators. We
introduce two adaptive techniques aimed at building the restriction operators
according to the properties of the system at hand. The proposed block
preconditioner has been tested through an extensive experimentation on both
synthetic and real-case applications, pointing out its robustness and
computational efficiency
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
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