text.skipToContent text.skipToNavigation
background-image

IUTAM Symposium on Discretization Methods for Evolving Discontinuities Proceedings of the IUTAM Symposium held Lyon, France, 4 - 7 September, 2006

  • Erscheinungsdatum: 07.04.2010
  • Verlag: Springer-Verlag
eBook (PDF)
139,99 €
inkl. gesetzl. MwSt.
Sofort per Download lieferbar

Online verfügbar

IUTAM Symposium on Discretization Methods for Evolving Discontinuities

In recent years, discretization methods have been proposed which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field. It provides the most comprehensive coverage of state-of-the art numerical methods for treating discontinuities in mechanics.

Produktinformationen

    Format: PDF
    Kopierschutz: AdobeDRM
    Seitenzahl: 436
    Erscheinungsdatum: 07.04.2010
    Sprache: Englisch
    ISBN: 9781402065309
    Verlag: Springer-Verlag
    Serie: IUTAM Bookseries Vol.5
    Größe: 14695 kBytes
Weiterlesen weniger lesen

IUTAM Symposium on Discretization Methods for Evolving Discontinuities

" Conservation under Incompatibility for Fluid-Solid-Interaction Problems: the NPCL Method (p. 414-415)

E.H. van Brummelen and R. de Borst

Summary. Finite-element discretizations of ?uid-solid-interaction problems only trivially preserve the conservation properties of the underlying problem under restrictive compatibility conditions on the approximation spaces for the ?uid and the solid. The present work introduces a new general method for enforcing interface conditions that maintains the conservation properties under incompatibility. The method is based on a nonlinear variational projection of the velocity ?eld to impose the kinematic condition, and a consistent evaluation of the load functional that accounts for the dynamic condition. Numerical results for a projection problem are presented to illustrate the properties of the method.

Key words: ?uid-solid interaction, incompatibility, conservation, space-time ?niteelement methods.

1 Introduction

The numerical solution of ?uid-solid-interaction problems has prominence in many scienti?c and engineering disciplines. The interaction is induced by interface conditions, which prescribe continuity of displacements and tractions across the ?uid-solid interface. If the approximation spaces for the ?uid and the solid in the discretization are compatible, i.e., if the ?uid and the solid have identical meshes and orders of approximation at the interface, then the enforcement of these continuity requirements is trivial. However, in many instances, it is necessary to allow for incompatible approximation spaces.

For instance, the meshes for the ?uid and solid subsystems may have been generated by di?erent analysts. Moreover, the disparate regularity properties of the ?uid and solid solutions typically prompt distinct approximation spaces. An important characteristic of ?uid-solid-interaction problems pertains to their conservation properties: on account of the continuity of tractions and displacements, mass, momentum and energy are conserved at the interface and, accordingly, the interface does not appear in the conservation statements for the aggregated system.

However, incompatibility impedes continuity of tractions and displacements across the interface in the discrete approximation. Consequently, incompatible ?nite-element discretizations of ?uid-solidinteraction problems do not generally preserve the conservation properties of the underlying continuum problem. Current coupling strategies for ?uid-solid interaction are in general nonconservative.

The change in a conserved quantities in the interior of the ?uid and solid domains via the interface can be expressed as an inner product on the interface. Conservation requires that this inner products evaluates to the same value at both sides of the interface. Most coupling methods however fail to identify the inner products. The methodology presented in [3] identi?es the inner products, but the inner products do not properly represent the change in the interior of the domains.

In this work we present a new general coupling method for ?uid-solidinteraction problems that preserves the conservation properties under incompatibility. The method comprises three complementary primitives: a suitable nonlinear variational projection to impose the kinematic condition, representation of the load functional in the velocity trace space of the ?uid, and a consistent evaluation of the load functional to account for the dynamic condition. We refer to the approach concisely as the NPCL (Nonlinear variational Projection with Consistent Loading) method."

Weiterlesen weniger lesen

Kundenbewertungen