FINITE ELEMENT TECHNIQUES FOR FLUID FLOW
1 GOVERNING EQUATIONS OF FLUID MECHANICS 11 FLUID PARTICLE 12 MATHEMATICAL DESCRIPTION OF FLUID FLOW 13 TRANSPORT THEOREM 131 SURFACE INTEGRAL FORM 132 DIVERGENCE FORM 14 FLOWING AND STATIONARY FLUID VOLUMES 15 STRESS TENSOR 151 GEOMETRY OF A TETRAHEDRON SURFACE TRACTION STRESS TENSOR SYMMETRY NORMAL STRESSES STRESS INVARIANT, MECHANICAL PRESSURE AND DEVIATORIE STRESSES 16 FLOW STATE VARIABLES FUNDAMENTAL EQUATIONS 171 CONSERVATION OF MASS: THE CONTINUITY EQUATION 172 SECOND LAW OF MECHANICS: THE LINEAR MOMENTUM EQUATION 173 THE FIRST LAW OF THERMODYNAMIES: THE TOTAL ENERGY EQUATION 18 CONSEQUENCES OF MASS CONSERVATION 181 182 SUBSTANTIVE-DERIVATIVE FORM OF THE TRANSPORT THEOREM 183 INTERCHANGE OF DIFFERENTIATION ORDER FOR MASS AND TIME VELOCITY DIVERGENCE 191 PHYSICAL SIGNIFICANCE 192 EQUATIONS FOR A FLUID PARTICLE 110 ENERGY EQUATIONS 1101 KINETIE ENERGY EQUATION 1102 RIGID-MOTION AND DEFORMATION WORK 1103 INTERNAL ENERGY EQUATION 1104 ENTROPY EQUATION 1105 TOTAL ENTHALPY EQUATION 1106 INTERNAL ENTHALPY AND TEMPERATURE EQUATIONS 111 SPECIAL SOLUTIONS OF THE INTERNAL-ENERGY, ENTHALPY, AND MOMENTUM EQUATIONS SUBSTANTIVE DERIVATIVE 1111 ISENTROPIE SOLUTION OF THE INTERNAL ENERGY EQUATION 1112 ADIABATIC- AND INVISCID-FLOW SOLUTION OF THE TOTAL-ENTHALPY EQUATION 1113 ISENTROPIE SOLUTION OF THE MOMENTUM EQUATION 2 CONSTITUTIVE AND STATE EQUATIONS 21 NAVIER-STOKES STRESS TENSOR 22 HEAT CONDUCTION LAW 23 TRANSPORT AND THERMO-MECHANICAL PROPERTIES 24 SECOND-LAW CONSTRAINTS ON TRANSPORT COEFFICIENTS 25 EQUATIONS OF STATE 26 SPEED OF SOUND 27 ISENTROPIE CONSTRAINT ON DERIVATIVES OF DENSITY AND ENERGY 3 STATE EQUATIONS FOR REACTING AIR 31 THERMO-CHEMICAL EQUATIONS 311 SPECIES MASSES AND MOLES 312 MASS AND MOLE FRACTIONS 313 PRESSURE, INTERNAL-ENERGY, MASS-FRACTION EQUATIONS 314 PERFECT-AIR EQUATIONS 315 NON-DIMENSIONAL REACTING-AIR EQUATIONS OF STATE 316 CHEMICAL AND THERMODYNAMIES PARAMETERS 317 CHEMICAL EQUILIBRIUM FUNETIONS 32 ALGEBRAIE SOLUTION CALCULATION OF Y3 AND T 331 NUMERICAL SOLUTION 332 ITERATION PARTIAL DERIVATIVES 34 PARTIAL DERIVATIVES OF T, Y1, Y2, Y3 , Y4, YS WITH RESPECT TO P AND € 341 DERIVATIVES OF T AND Y3 342 DERIVATIVES OF Y1, Y2, Y4, Y5 PRESSURE AND ITS THERMODYNAMIE DERIVATIVES JACOBIAN PARTIAL DERIVATIVES OF PRESSURE AND TEMPERATURE 37 DERIVATIVES OF P AND Y, WITH RESPECT TO P, T, DERIVATIVES OF P WITH RESPEET TO P AND T, AND DERIVATIVES OF T WITH RESPECT TO P AND P 38 THERMODYNAMIE PROPERTIES WITH P AND T AS INDEPENDENT VARIABLES 39 SPECIFIE HEATS 391 SPECIFIC HEAT C 392 SPECIFIE HEAT CP 310 SPEED OF SOUND 311 COMPUTATIONAL RESULTS 312 PERFORMANCE SUMMARY 4 EULER AND NAVIER STOKES SYSTEMS 41 COMPRESSIBLE FLOWS 411 CONSERVATION FORM 412 NON-DIMENSIONAL SYSTEM 413 VARIATIONAL FORMULATION 42 LOW SPEED AND INCOMPRESSIBLE FLOWS CONTINUITY EQUATION MOMENTUM EQUATION TEMPERATURE EQUATION GOVERNING SYSTEM NON-DIMENSIONAL SYSTEM VARIATIONAL FORMULATION 5 QUASI ONE-DIMENSIONAL AND FREE-SURFACE EQUATIONS 51 AREA AVERAGES 52 QUASI ONE-DIMENSIONAL EULER EQUATIONS 521 CONTINUITY EQUATION 522 GENERALIZED LINEAR-MOMENTUM EQUATION 523 ENERGY EQUATION 524 COMPRESSIBLE-FLOW SYSTEM 525 INCOMPRESSIBLE-FLOW SYSTEM OPEN-CHANNEL CONFIGURATION 531 DEPTH AVERAGES 532 AREA AVERAGES QUASI ONE-DIMENSIONAL FREE-SURFACE OPEN-CHANNEL FLOW EQUATIONS CONTINUITY EQUATION MOMENTUM EQUATION ENERGY EQUATION QUASI ONE-DIMENSIONAL FREE-SURFACE SYSTEM 55 TWO-DIMENSIONAL FREE-SURFACE EQUATIONS CONTINUITY EQUATION MOMENTUM EQUATION ENERGY EQUATION 554 NON-DIMENSIONAL 2-D FREE-SURFACE EQUATIONS 6 OVERVIEW OF CFD ALGORITHM DEVELOPMENT 61 MATHEMATICAL MODEL 62 SPATIAL APPROXIMATION: DISERETIZATION 621 STEADY-SOLUTION MONOTONICITY 622 UNSTEADY-SOLUTION STABILITY 63 TIME INTEGRATION 64 SOLUTION OF NON-LINEAR SYSTEMS 7 THE FINITE ELEMENT METHOD 71 VARIATIONAL WEIGHTED INTEGRAL STATEMENTS 711 LEAST SQUARES STATEMENTS 712 REPRESENTATIVE OPTIMAL SOLUTIONS 713 FLUID DYNAMIES EQUATIONS FROM A VARIATIONAL PRINCIPLE 72 INTEGRALS FROM GAUSS' DIVERGENCE THEOREM