PRESENTATION DE LA METHODE DE BRILEY ET MCDONALD UTILISANT UN SCHEMA IMPLICITE RETARDE EN TEMPS; LES TERMES D'ESPACE SONT LINEARISES PAR UN DEVELOPPEMENT DE TAYLOR, PUIS DISCRETISES PAR DES SCHEMAS AUX DIFFERENCES, CENTRES POUR LES DERIVEES PREMIERES; LE SYSTEME D'EQUATIONS COUPLEES EN RESULTANT EST TRAITE SOUS UNE FORME MODIFIEE, PAR UNE METHODE DE DIRECTION ALTERNEE. CETTE METHODE EST ETENDUE A DES COORDONNEES CYLINDRIQUES AVEC, DE PLUS, UNE TRANSFORMATION RADIALE, POUVANT ETRE QUELCONQUE ET PERMETTANT DE FAIRE VARIER LA DENSITE DU MAILLAGE SUIVANT LE RAYON DE FACON A L'ADAPTER A CHAQUE PROBLEME TRAITE. LES EQUATIONS RESOLUES SONT PLUS GENERALES QUE CELLES DE BRILEY ET MCDONALD CAR LES COEFFICIENTS DE VISCOSITE ET DE CONDUCTION THERMIQUE NE SONT PLUS FIXES MAIS PEUVENT SUIVRE TOUTE LOI VOULUE

With the advent of super computers during the last ten years, the numerical simulation of viscous fluid flows modeled by the Navier-Stokes equations is becoming a most useful tool in Aircraft and Engine Design. In fact, compressible Navier-Stokes solvers tend to constitute the basic tools for many industrial applications occuring in the simulation of very complex turbulent and combustion phenomena. In Aerospace Engineering, as an exemple, their mathematical modelization requires reliable and robust methods for solving very stiff non linear partial differential equations. For the above reasons, it was clear that a workshop on this topic would be of interest for the CFD community in order to compare accuracy and efficiency of Navier-Stokes solvers on selected external and internal flow problems using different numerical approaches. The workshop was held on 4-6 December 1985 at Nice, France and organized by INRIA with the sponsorship of the GAMM Committee on Numerical Methods in Fluid Mechanics.

ON RECHERCHE LES PERFORMANCES D'UN SCHEMA AUX DIFFERENCES FINIES DU TYPE SEMI-IMPLICITE POUR LA RESOLUTION DES EQUATIONS DE NAVIER STOKES POUR LES FLUIDES COMPRESSIBLES. ON COMPARE CE SCHEMA AVEC QUELQUES SCHEMAS PROPOSES POUR CE PROBLEME. ON APPLIQUE LE SCHEMA SEMI IMPLICITE A L'ETUDE DE L'ECOULEMENT SUPERSONIQUE PLAN A FAIBLE NOMBRE DE REYNOLDS SUR UN OBSTACLE DE SECTION ELLIPTIQUE.

In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.