An Introduction to Computational Fluid Mechanics by Example

AN INTRODUCTION TOCOMPUTATIONAL FLUIDMECHANICS BY EXAMPLE......Page 1
2 Inviscid Fluid Flows 50......Page 5
Bibliography 298 Index 303......Page 6
PREFACE......Page 7
1.1 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS: INITIAL-VALUE PROBLEMS......Page 9
1.2 FREE FALLING OF A SPHERICAL BODY......Page 13
1.3 COMPUTER SIMULATION OF SOME RESTRAINED MOTIONS......Page 21
1.4 FOURTH-ORDER RUNGE-KUTTA METHOD FOR COMPUTING TWO-DIMENSIONAL MOTIONS OF A BODY THROUGH A FLUID......Page 30
1.5 BALLISTICS OF A SPHERICAL PROJECTILE......Page 32
1.6 FLIGHT PATH OF A GLIDER - A GRAPHICAL PRESENTATION......Page 40
1.7 ROLLING UP OF THE TRAILING VORTEX SHEET BEHIND A FINITE WING......Page 43
APPENDIX......Page 52
2. INVISCID FLUID FLOWS......Page 58
2.1 INCOMPRESSIBLE POTENTIAL FLOWS......Page 59
2.2 NUMERICAL SOLUTION OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS: BOUNDARY-VALUE PROBLEMS......Page 63
2.3 RADIAL FLOW CAUSED BY DISTRIBUTED SOURCES AND SINKS......Page 68
2.4 INVERSE METHOD I: SUPERPOSITION OF ELEMENTARY FLOWS......Page 69
2.5 VON KARMAN\'S METHOD FOR APPROXIMATING FLOW PAST BODIES OF REVOLUTION......Page 77
2.6 INVERSE METHOD II: CONFORMAL MAPPING......Page 84
2.7 CLASSIFICATION OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS......Page 95
2.8 NUMERICAL METHODS FOR SOLVING ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS......Page 98
2.9 POTENTIAL FLOWS IN DUCTS OR AROUND BODIES - IRREGULAR AND DERIVATIVE BOUNDARY CONDITIONS......Page 104
2.10 NUMERICAL SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS......Page 113
2.11 PROPAGATION AND REFLECTION OF A SMALL-AMPLITUDE WAVE......Page 118
2.12 PROPAGATION OF A FINITE-AMPLITUDE WAVE: FORMATION OF A SHOCK......Page 128
2.13 AN APPLICATION TO BIOLOGICAL FLUID DYNAMICS: FLOW IN AN ELASTIC TUBE......Page 136
APPENDIX......Page 151
3.1 GOVERNING EQUATIONS FOR VISCOUS FLOWS......Page 153
3.2 SELF-SIMILAR LAMINAR BOUNDARY-LAYER FLOWS......Page 155
3.3 FLAT-PLATE THERMOMETER PROBLEM—ORDINARY BOUNDARY-VALUE PROBLEMS INVOLVING DERIVATIVE BOUNDARY CONDITIONS......Page 165
3.4 PIPE AND OPEN-CHANNEL FLOWS......Page 171
3.5 EXPLICIT METHODS FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS - ENERALIZED RAYLEIGH PROBLEM......Page 176
3.6 IMPLICIT METHODS FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS - TARTING FLOW IN A CHANNEL......Page 181
3.7 NUMERICAL SOLUTION OF BIHARMONIC EQUATIONS - STOKES FLOWS......Page 187
3.8 FLOW STABILITY AND PSEUDO-SPECTRAL METHODS......Page 193
APPENDIX......Page 215
4. NUMERICAL SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATION......Page 223
4.1 FLOW AROUND A SPHERE AT FINITE REYNOLDS NUMBERS - ALERKIN METHOD......Page 224
4.2 UPWIND DIFFERENCING AND ARTIFICIAL VISCOSITY......Page 237
4.3 BENARD AND TAYLOR INSTABILITIES......Page 242
4.4 PRIMITIVE VARIABLE FORMULATION: ALGORITHMIC CONSIDERATIONS......Page 257
4.5 PRIMITIVE VARIABLE FORMULATION: NUMERICAL INTEGRATION OF THE NAVIER-STOKES EQUATION......Page 266
4.6 FLOW PAST A CIRCULAR CYLINDER: AN EXAMPLE FOR THE VORTICITY-STREAM FUNCTION FORMULATION......Page 288
APPENDIX......Page 305
BIBLIOGRAPHY......Page 306
INDEX......Page 311