COMPUTATIONAL FLUID MECHANICS AND HEAT TRANSFER
CONTENTS INTRODUCTION PRELIMINARIES AVAILABLE TOOLS FOR THE ENGINEER CLASSES OF NUMERICAL METHODS AVAILABLE OBJECTIVES AND SCOPE OF THIS BOOK APPLICATIONS OF COMPUTATIONAL FLUID DYNAMICS REFERENCE CONSERVATION EQUATIONS—PHYSICAL AND MATHEMATICAL ASPECTS MODELS FORMULATION LEVELS CONSERVATION EQUATIONS MASS CONSERVATION EQUATION LINEAR MOMENTUM CONSERVATION EQUATIONS ENERGY CONSERVATION EQUATION ELLIPTIC, PARABOLIC AND HYPERBOLIC PROBLEMS PARABOLIC AND HYPERBOLIC PROBLEMS ELLIPTIC PROBLEMS TRUE AND DISTORTED TRANSIENT CONCLUSIONS EXERCISES REFERENCES THE FINITE VOLUME METHOD THE TASK OF A NUMERICAL METHOD WHY FINITE VOLUME METHODS IS A GOOD CHOICE FEW WORDS ABOUT THE CONSERVATIVE PROPERTY CELL-CENTER AND CELL-VERTEX METHODS ONE DIMENSIONAL TRANSIENT HEAT DIFFUSION EXPLICIT, IMPLICIT AND FULLY IMPLICIT FORMULATIONS EXPLICIT FORMULATION FULLY IMPLICIT FORMULATION IMPLICIT FORMULATION LINEARIZATION OF THE SOURCE TERM BOUNDARY CONDITIONS BALANCES FOR THE BOUNDARY VOLUMES USING FICTITIOUS VOLUMES ABOUT BOUNDARY CONDITIONS IN CELL-VERTEX DISCRETIZATION OF THE 3D DIFFUSION EQUATION STRUCTURE OF THE MATRIX OF COEF?CIENTS HANDLING NON-LINEARITIES RELEVANT ISSUES WHEN DISCRETIZING THE EQUATIONS POSITIVITY OF COEF?CIENTS FLUXES CONTINUITY AT INTERFACES LINEARIZATION OF SOURCE TERM WITH SP NEGATIVE TRUNCATION ERRORS CONSISTENCY, STABILITY AND CONVERGENCE SOLUTION OF THE LINEAR SYSTEM ITERATIVE METHODS JACOBI GAUSS-SEIDEL SOR-SUCCESSIVE OVER RELAXATION ALTERNATING DIRECTION IMPLICIT METHODS INCOMPLETE LU DECOMPOSITION A NOTE ON CONVERGENCE OF ITERATIVE METHODS MULTIGRID METHOD ADVECTION AND DIFFUSION—INTERPOLATION FUNCTIONS THE GENERAL EQUATION THE DIF?CULTY OF THE ADVECTIVE-DOMINANT PROBLEM INTERPOLATION FUNCTIONS FOR ? THE PHYSICS BEHIND THE INTERPOLATION FUNCTIONS ONE DIMENSIONAL INTERPOLATION FUNCTIONS NUMERICAL OR FALSE DIFFUSION TWO AND THREE-DIMENSIONAL INTERPOLATION FUNCTIONS THREE-DIMENSIONAL ADVECTION/DIFFUSION OF ? INTEGRATION OF THE 3D EQUATION FOR ? TRUE TRANSIENT DISTORTED TRANSIENT FINDING THE VELOCITY FIELD—PRESSURE/VELOCITY COUPLINGS SYSTEM OF EQUATIONS ABOUT SEGREGATED AND SIMULTANEOUS SOLUTION SEGREGATED FORMULATION INCOMPRESSIBILITY VARIABLE ARRANGEMENT ON THE GRID CO-LOCATED GRID ARRANGEMENT STAGGERED GRID ARRANGEMENT CO-LOCATED PV COUPLING (CPVC) METHODS RHIE AND CHOW-LIKE METHODS PIS—PHYSICAL IN?UENCE SCHEME SEGREGATED PV COUPLING (SPVC) METHODS CHORIN’S METHOD SIMPLE—SEMI IMPLICIT LINKED EQUATIONS SIMPLER—SIMPLE-REVISITED PRIME—PRESSURE IMPLICIT MOMENTUM EXPLICIT SIMPLEC—SIMPLE CONSISTENT PISO—PRESSURE IMPLICIT WITH SPLIT OPERATOR SIMPLEC FOR CO-LOCATED GRIDS PRIME FOR CO-LOCATED GRIDS BOUNDARY CONDITIONS FOR P AND P' SIMULTANEOUS SOLUTION AND THE COUPLINGS A NOTE ON BOUNDARY CONDITIONS IMPERMEABLE BOUNDARY—? PRESCRIBED IMPERMEABLE BOUNDARY—FLUX OF ? PRESCRIBED IN?OW AND OUT?OW BOUNDARY CONDITIONS GENERAL COMMENTS ABOUT BOUNDARY CONDITIONS INCOMPRESSIBLE FLOWS COMPRESSIBLE FLOWS ALL SPEED FLOWS CALCULATION—COUPLING P ?[V ? ?] PRESSURE–VELOCITY AND PRESSURE-DENSITY COUPLING LINEARIZATION OF THE MASS FLOW TWO-DIMENSIONAL ALL SPEED FLOW DISCRETIZATION VELOCITY RELATIONS AS FUNCTION OF P'- SIMPLEC DENSITY RELATIONS AS FUNCTION OF P'- SIMPLEC VELOCITY/DENSITY RELATIONS AS FUNCTION OF P-PRIME TWO AND THREE-DIMENSIONAL PARABOLIC FLOWS TWO-DIMENSIONAL PARABOLIC FLOWS EXTERNAL TWO-DIMENSIONAL PARABOLIC FLOWS INTERNAL TWO-DIMENSIONAL PARABOLIC FLOWS THREE-DIMENSIONAL PARABOLIC FLOWS EXTERNAL THREE-DIMENSIONAL PARABOLIC FLOWS INTERNAL THREE-DIMENSIONAL PARABOLIC FLOWS GENERAL RECOMMENDATIONS FOR CONCEIVING AND TESTING YOUR CODE WRITING YOUR CODE GENERALITIES CODING LANGUAGES TOOLS TO AID THE DEVELOPMENT RUNNING YOUR APPLICATION COMPILING SIZE OF THE MESH CONVERGENCE CRITERIA CHOOSING TEST PROBLEMS—FINDING ERRORS HEAT CONDUCTION—2D STEADY STATE TRANSIENT HEAT CONDUCTION—ONE DIMENSIONAL ONE DIMENSIONAL ADVECTION/DIFFUSION TWO-DIMENSIONAL ADVECTION/DIFFUSION ENTRANCE FLOW BETWEEN PARALLEL PLATES OBSERVING DETAILS OF THE SOLUTION SYMMETRY OF THE SOLUTION THE COEF?CIENTS TESTING THE SOLVER OF THE LINEAR SYSTEM INTRODUCING GENERAL GRIDS DISCRETIZATION STRUCTURED AND NON-STRUCTURED GRIDS THE CONCEPT OF ELEMENT CONSTRUCTION OF THE CONTROL VOLUME COORDINATE TRANSFORMATION—GENERAL CURVILINEAR COORDINATE SYSTEMS GLOBAL COORDINATE TRANSFORMATION GENERAL LENGTH ALONG A COORDINATE AXIS AREAS (OR VOLUMES) IN THE CURVILINEAR SYSTEM BASIS VECTORS VECTOR REPRESENTATION IN THE CURVILINEAR SYSTEM MASS FLOW CALCULATION EXAMPLE OF A NONORTHOGONAL TRANSFORMATION CALCULATION OF THE METRICS OF A TRANSFORMATION NATURE OF THE DISCRETE TRANSFORMATION THE NATURE OF THE TRANSFORMATION EQUATIONS WRITTEN IN THE CURVILINEAR SYSTEM DISCRETIZATION OF THE TRANSFORMED EQUATIONS COMMENTS ON THE SOLUTION OF THE EQUATION SYSTEM SIMULTANEOUS SOLUTION SEGREGATED SOLUTION NO-FLOW BOUNDARY (?U = 0) ? PRESCRIBED NO-FLOW BOUNDARY (?U = 0) FLUX OF ? PRESCRIBED BOUNDAY WITH MASS FLOW (?U /= 0) MASS ENTERING WITH ?U KNOWN BOUNDARY WITH MASS FLOW (?U /= 0) MASS LEAVING WITH ?U UNKNOWN UNSTRUCTURED GRIDS CELL-CENTER METHODS CONVENTIONAL FINITE VOLUME METHOD VORONOI DIAGRAMS EBFVM—ELEMENT-BASED FINITE VOLUME METHOD GEOMETRICAL ENTITIES LOCAL COORDINATES SHAPE FUNCTIONS DETERMINATION OF (??)IP DETERMINATION OF ?IP FAMILY OF POSITIVE ADVECTION SCHEMES INTEGRATION OF THE CONSERVATION EQUATIONS ASSEMBLING STRATEGIES PRESSURE INSTABILITIES: FROM NAVIER–STOKES TO POROELASTICITY PRESSURE INSTABILITIES REMEDY 1 REMEDY 2 APPLICATIONS AERODYNAMICS ALL SPEED FLOW OVER A BLUNT BODY ICE ACCRETION ON AERODYNAMIC PRO?LES POROUS MEDIA FLOWS