Abgrall, Rémi

Guillard, Hervé

Numérisation de Documents Anciens Mathématiques

ESAIM: M2ANVol. 39, No 3, 2005, p. 437DOI: 10.1051/m2an:2005018ForewordLow Mach Number Flows ConferenceLow Mach number ﬂows represent a signiﬁcant part of the various ﬂows encountered in geophysics, industryor every day life. Paradoxically, the mathematical analysis of the equations governing these ﬂows is diﬃcult andon the practical side, the research of numerical algorithms valid for all ﬂow speeds is continuing to be a challenge.However, in the last decade, both from the theoretical and the numerical sides, signiﬁcant progresses havebeen made in the understanding, analysis and approximation of the equations governing these ﬂows.This has motivated us to organize in June 21-25 2004 on the Porquerolles Island, an international conferencein order to provide an up–to–date inventory of the recent mathematical and numerical results in the analysis ofthese ﬂows. This special issue gathers some contributions from the papers presented at this conference. Theirtopics range from theoretical analysis of PDEs (contributions of S. Schochet, R. Danchin, D. Bresch et al.)to the design of numerical schemes (contributions of S. Dellacherie, E. Turkel et al., R. Klein, and S. Rolleret al.). This gives a good example of the fruitful interactions between mathematicians and numericists that thisconference has generated. The conference also included a numerical workshop proposing to compute severalchallenging low Mach number ﬂows. The results of this workshop are included in this volume as a testimony of2004 state–of–the–art methods in the approximation of these ﬂows (contributions of F. Beux et al., S. Vincentet al., P. Le Que´re´ et al. and H. Paille`re et al.).The ﬁnancial support of CNRS, INRIA, Institut de Radioprotection et Suˆrete´ Nucle´aire (IRSN) and InstitutUniversitaire de France is acknowledged. Last we thank the scientiﬁc committee (Tanh-Ha Nguyen-Bui fromCEA, CESTA, Benoit Desjardins from CEA, Bruye`res-le-Chatel, Jean-Claude Latche´ from Institut de Radio-protection et Suˆrete´ Nucle´aire, Cadarache and Guy Me´tivier, Mathe´matiques Applique´es de Bordeaux I andInstitut Universitaire de France) as well as all the referees that have critically examined these papers.Re´mi Abgrall1, Herve´ Guillard21Mathe´matiques Applique´es de Bordeaux, UMR CNRS 5466 and Institut Universitaire de France.2INRIA Sophia Antipolis.c© EDP Sciences, SMAI 2005Article published by EDP Sciences and available at http://www.edpsciences.org/m2an or http://dx.doi.org/10.1051/m2an:2005018

Foreword. Low Mach number flows conference

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Numérisation de Documents Anciens Mathématiques