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Integration of the EPDiff equation by particle methods

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that is well-suited for this class of solutions and...

Integration of the EPDiff equation by particle methods∗∗∗∗∗∗

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that...

Interaction of compressible flow with an airfoil

Česenek, Jan, Feistauer, Miloslav (2010)

Programs and Algorithms of Numerical Mathematics

The paper is concerned with the numerical solution of interaction of compressible flow and a vibrating airfoil with two degrees of freedom, which can rotate around an elastic axis and oscillate in the vertical direction. Compressible flow is described by the Navier-Stokes equations written in the ALE form. This system is discretized by the semi-implicit discontinuous Galerkin finite element method (DGFEM) and coupled with the solution of ordinary differential equations describing the airfoil motion....

Internal constraints and linear constitutive relations for transversely isotropic materials

Paolo Podio-Guidugli, Maurizio Vianello (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

All internal constraints compatible with transverse isotropy are determined and representation formulae are given for the constitutive relations of arbitrarily constrained, transversely isotropic materials.

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