CETTE THESE EST CONSACREE A L'ETUDE DES REGIMES TRANSITOIRES D'ECOULEMENTS DIPHASIQUES A FAIBLE RAPPORT DE DENSITES, C'EST A DIRE QUAND LA PHASE GAZEUSE, COMPRESSIBLE, EST BEAUCOUP PLUS LEGERE QUE LA PHASE LIQUIDE. TOUT D'ABORD, NOUS PRESENTONS BRIEVEMENT LE CONTEXTE : MODELISATION DIPHASIQUE, NOTION D'HYPERBOLICITE ET METHODE DES VOLUMES FINIS. DANS UNE SECONDE PARTIE NOUS ETUDIONS LA STRUCTURE SPECTRALE DES MATRICES JACOBIENNES DES SYSTEMES BI-FLUIDES. NOUS PROPOSONS D'INTRODUIRE LE RAPPORT DES DENSITES COMME PETIT PARAMETRE PUIS UTILISONS DES METHODES DE PERTURBATION POUR ANALYSER LES ELEMENTS PROPRES DE CES MATRICES. DE CETTE MANIERE, NOUS MONTRONS COMMENT, SELON LES MODELES, CES MATRICES PEUVENT ETRE DIAGONALISABLES A VALEURS PROPRES REELLES, COMPLEXES, OU BIEN JORDANISABLES. LA TROISIEME PARTIE EST CONSACREE A LA PROGRAMMATION DE LA METHODE DES VOLUMES FINIS DANS CE CONTEXTE EN MAILLAGE NON-STRUCTURE MULTIDIMENSIONNEL. LES RESULTATS SONT VALIDES SUR DES CAS TESTS POUR DES ECOULEMENTS EN DESEQUILIBRE PAR COMPARAISON AVEC L'EXPERIENCE MAIS AUSSI SUR DES CAS TESTS ORIGINAUX PAR RAFFINEMENT DE MAILLAGE. DANS UNE DERNIERE PARTIE, NOUS CONSTATONS QUE L'ADIMENSIONNALISATION DES DENSITES MET EN EVIDENCE LA RAIDEUR DE CERTAINS TERMES SOURCES DE RELAXATION. NOUS ETUDIONS LA DYNAMIQUE ASSOCIEE PAR ANALYSE DE STABILITE LINEAIRE ET DEVELOPPEMENT DE CHAPMAN-ENSKOG. BIEN QUE LES JACOBIENNES DU SYSTEME NE SOIENT PLUS DIAGONALISABLES A LA LIMITE NOUS MONTRONS LA STABILITE LINEAIRE FAIBLE DES REGIMES LIMITES ET CONFIRMONS CETTE APPROCHE PAR NOS RESULTATS NUMERIQUES.

DESCRIPTION DU PHENOMENE DE CHOUCAGE (ECOULEMENT DIPHASIQUE PULSE, AUTO-ENTRETENU, A BASSE FREQUENCE, QUI PREND NAISSANCE DANS UN CANAL VERTICAL CHAUFFE A PUISSANCE DISSIPEE CONSTANTE ET ALIMENTE EN LIQUIDE A SA PARTIE INFERIEURE). IL EST LIE AUX PROBLEMES DE SURETE DES REACTEURS A EAU ET SODIUM. LES MODELES UTILISES POUR DECRIRE CES ECOULEMENTS ET ETUDIER LEUR STABILITE SONT NON LINEAIRES, DISTRIBUES ET COMPORTENT PLUSIEURS VARIABLES D'ETAT ET DES FRONTIERES LIBRES. ON PROPOSE UNE MODELISATION STATISTIQUE DE L'EVALUATION DE CERTAINS ENSEMBLES DE PARTICULES, QUI S'APPLIQUE A L'EBULLITION SOUS-SATUREE DANS UN CANAL EN REGIME TRANSITOIRE, ET ON DETERMINE LA STRUCTURE DES LOIS D'ECHANGE AVEC LA PAROI POUR LA FORMULATION MONODIMENSIONNELLE DES ECOULEMENTS LAMINAIRES EN CONDUITE CYLINDRIQUE

The proceedings of the 9th conference on "Finite Volumes for Complex Applications" (Bergen, June 2020) are structured in two volumes. The first volume collects the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Topics covered include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. Altogether, a rather comprehensive overview is given on the state of the art in the field. The properties of the methods considered in the conference give them distinguished advantages for a number of applications. These include fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory, carbon capture utilization and storage, geothermal energy and further topics. The second volume covers reviewed contributions reporting successful applications of finite volume and related methods in these fields. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability, making the finite volume methods compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.

This book is a collection of extended papers based on presentations given during the SIMHYDRO 2014 conference, held in Sophia Antipolis in June 2014. It focuses on the modeling and simulation of fast hydraulic transients, on 3D modeling, and on uncertainties and multiphase flows. The book explores both the limitations and performance of current models and presents the latest developments based on new numerical schemes, high-performance computing, multiphysics and multiscale methods, and better interaction with field or scale model data. It addresses the interests of practitioners, stakeholders, researchers and engineers active in this field.