GENERALIZED RIEMANN PROBLEMS IN COMPUTATIONAL FLUID DYNAMICS

By C. KURAY

CONTENTS INTRODUCTION I BASIC THEORY SCALAR CONSERVATION LAWS THEORETICAL BACKGROUND BASIC CONCEPTS OF NUMERICAL APPROXIMATION THE GRP METHOD FOR SCALAR CONSERVATION LAWS FROM GODUNOV TO THE GRP METHOD 1-D SAMPLE PROBLEMS THE LINEAR CONSERVATION LAW THE BURGERS NONLINEAR CONSERVATION LAW 2-D SAMPLE PROBLEMS SYSTEMS OF CONSERVATION LAWS NONLINEAR HYPERBOLIC SYSTEMS IN ONE SPACE DIMENSION EULER EQUATIONS OF QUASI-1-D, COMPRESSIBLE, INVISCID FLOW THE GENERALIZED RIEMANN PROBLEM (GRP) FOR COMPRESSIBLE FLUID DYNAMICS THE GRP FOR QUASI-1-D, COMPRESSIBLE, INVISCID FLOW THE GRP NUMERICAL METHOD FOR QUASI-1-D, COMPRESSIBLE, INVISCID FLOW VII ANALYTICAL AND NUMERICAL TREATMENT OF FLUID DYNAMICAL PROBLEMS THE SHOCK TUBE PROBLEM WAVE INTERACTIONS SHOCK–CONTACT INTERACTION SHOCK–SHOCK INTERACTION SHOCK–CRW INTERACTION CRW–CONTACT INTERACTION SPHERICALLY CONVERGING FLOW OF COLD GAS THE FLOW INDUCED BY AN EXPANDING SPHERE CONVERGING–DIVERGING NOZZLE FLOW II NUMERICAL IMPLEMENTATION FROM THE GRP ALGORITHM TO SCIENTI?C COMPUTING GENERAL DISCUSSION STRANG’S OPERATOR-SPLITTING METHOD TWO-DIMENSIONAL FLOW IN CARTESIAN COORDINATES GEOMETRIC EXTENSIONS GRIDS THAT MOVE IN TIME SINGULARITY TRACKING MOVING BOUNDARY TRACKING (MBT) BASIC SETUP SURVEY OF THE FULL MBT ALGORITHM AN EXAMPLE: SHOCK LIFTING OF AN ELLIPTIC DISK A PHYSICAL EXTENSION: REACTING FLOW THE EQUATIONS OF COMPRESSIBLE REACTING FLOW THE CHAPMAN–JOUGUET (C–J) MODEL THE Z–N–D (ZELDOVICH–VON NEUMANN–D¨ORING) SOLUTION THE LINEAR GRP FOR THE REACTING-FLOW SYSTEM THE GRP SCHEME FOR REACTING FLOW WAVE INTERACTION IN A DUCT – A COMPARATIVE STUDY