ON S'INTERESSE DANS CETTE THESE A L'ETUDE DES SYSTEMES HYPERBOLIQUES DE LOIS DE CONSERVATION NON-LINEAIRES AVEC TERMES SOURCES. D'UN POINT DE VUE THEORIQUE, ON COMMENCE PAR ETUDIER LE PROBLEME DE RIEMANN GENERALISE. ENSUITE, ON MONTRE QU'UNE CONDITION SUFFISANTE DE CONVERGENCE DES APPROXIMATIONS VISQUEUSES POUR UNE LOI SCALAIRE NON-HOMOGENE EST D'ASSURER UNE ESTIMATION UNIFORME EN AMPLITUDE. LE PROBLEME EST PLUS DELICAT POUR UN SYSTEME. L'ETUDE DES DISCRETISATIONS IMPLICITES D'UNE LOI SCALAIRE GENERALE MONTRE QU'IL EXISTE DES CONDITIONS DE TYPE CFL POUR GARANTIR L'INVERSIBILITE DU SCHEMA ET PREVENIR L'APPARITIONS D'OSCILLATIONS PARASITES DANS LA SOLUTION NUMERIQUE. ON INTRODUIT ENSUITE UN SCHEMA “WELL-BALANCED” AU SENS DE GREENBERG ET LEROUX CONVERGENT VERS LA SOLUTION ENTROPIQUE DANS LE CAS SCALAIRE. L'EXTENSION AUX SYSTEMES GENERAUX SE FAIT PAR LE BIAIS D'UNE REFORMULATION DES TERMES SOURCES EN PRODUITS NON-CONSERVATIFS. ON CALCULE ALORS UNE LINEARISEE DE TYPE ROE POUR LES EQUATIONS D'EULER NON-HOMOGENES. PAR SOUCI DE ROBUSTESSE, ON DERIVE AUSSI UN SCHEMA DE TYPE “DECOMPOSITION DE FLUX” NON-CONSERVATIF PERMETTANT D'APPROCHER DES SYSTEMES VARIES ET CONSISTANT AVEC LES LIMITES RELAXEES. DES TESTS SONT AUSSI EFFECTUES EN REGIME RESONANT ET POUR DES PROBLEMES DIPHASIQUES SIMPLIFIES BIDIMENSIONNELS.

This work traces the development of numerical methods for non-Newtonian flows from the late 1960s to 2001. It begins with broad coverage of non-Newtonian fluids, including their mathematical modelling and analysis, and then specific computational techniques are discussed.

Numerical Computation of Internal and External Flows Volume 2: Computational Methods for Inviscid and Viscous Flows C. Hirsch, Vrije Universiteit Brussel, Brussels, Belgium This second volume deals with the applications of computational methods to the problems of fluid dynamics. It complements the first volume to provide an excellent reference source in this vital and fast growing area. The author includes material on the numerical computation of potential flows and on the most up-to-date methods for Euler and Navier-Stokes equations. The coverage is comprehensive and includes detailed discussion of numerical techniques and algorithms, including implementation topics such as boundary conditions. Problems are given at the end of each chapter and there are comprehensive reference lists. Of increasing interest, the subject has powerful implications in such crucial fields as aeronautics and industrial fluid dynamics. Striking a balance between theory and application, the combined volumes will be useful for an increasing number of courses, as well as to practitioners and researchers in computational fluid dynamics. Contents Preface Nomenclature Part V: The Numerical Computation of Potential Flows Chapter 13 The Mathematical Formulations of the Potential Flow Model Chapter 14 The Discretization of the Subsonic Potential Equation Chapter 15 The Computation of Stationary Transonic Potential Flows Part VI: The Numerical Solution of the System of Euler Equations Chapter 16 The Mathematical Formulation of the System of Euler Equations Chapter 17 The Lax - Wendroff Family of Space-centred Schemes Chapter 18 The Central Schemes with Independent Time Integration Chapter 19 The Treatment of Boundary Conditions Chapter 20 Upwind Schemes for the Euler Equations Chapter 21 Second-order Upwind and High-resolution Schemes Part VII: The Numerical Solution of the Navier-Stokes Equations Chapter 22 The Properties of the System of Navier-Stokes Equations Chapter 23 Discretization Methods for the Navier-Stokes Equations Index

The principles and practice of finite volume method are highlighted in this book. In this book, readers will find a subject which will increase their interest and involve them to further explore a challenge and work further on the presented solutions. This book can serve the purposes of both; a textbook and a practical guide. It presents a vast variety of ideas in FVM which is a result of the efforts of scientists from across the world. The major topics covered in this book are novel techniques and algorithms in FVM, solution of particular problems through FVM and application of FVM in medicine and engineering. This book is for anyone who wants to grow, improve and explore.