Fluid Shock Wave Generation at Solid-Material Discontinuity Surfaces in Porous Media
A general set of boundary conditions at the interface between dissimilar fluid-filled porous matrices is established starting from an extended Hamilton-Rayleigh principle. These conditions do include inertial effects. Once linearized, they encompass bound
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CISM COURSES AND LECTURES
Series Editors: The Rectors Friedrich Pfeiffer - Munich Franz G. Rammerstorfer - Wien Jean Salençon - Palaiseau
The Secretary General
Executive Editor
The series presents lecture notes, monographs, edited works and and Applied Mathematics. ! and technical community results obtained in some of the activities " #$ % % &
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This volume contains 63 illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned $ broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2011 by CISM, Udine Printed in Italy SPIN 80124210
All contributions have been typeset by the authors.
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PREFACE
For this would be agreed by all: that Nature does nothing in vain nor labours in vain Olympiodorus, Commentary on Aristotle’s Meteora translated by Ivor Thomas in the Greek Mathematica Works Loeb Classical Library La nature, dans la production de ses effets, agit toujours par les voies les plus simples Pierre de Fermat
The CISM course C-1006 ”Variational models and methods in solid and fluid mechanics” was held July 12-16, 2010 in Udine, Italy. There were about forty five participants from different european countries. The papers included in this volume correspond to the content of five mini-courses of 6 hours each which have been delivered during this week. Variational formulation of the governing equations of solid and fluid mechanics is a classical but a very challenging topic. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers. This formulation allows for an easier justification of the well-posedness of mathematical problems, the study of stability of particular solutions, a simpler implementation of numerical methods. Often, mechanical problems are more naturally posed by means of a variational method. Hamilton’s principle of stationary (or least) action is the conceptual basis of practically all models in physics. The variational formulation is also useful for obtaining simpler approximate asymptotical models as done in the theory of homogeneization. In many problems of mechanics and physics, the functionals being minimized depend on parameters which can be considered as random
variables. Variational structure of such problems always brings considerable simplifications in their study. In this course, three fundamental aspects of the variati
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