APPLIED COMPUTATIONAL FLUID DYNAMICS TECHNIQUES

Transcription

1 APPLIED COMPUTATIONAL FLUID DYNAMICS TECHNIQUES AN INTRODUCTION BASED ON FINITE ELEMENT METHODS Second Edition Rainald Löhner Center for Computational Fluid Dynamics, Department of Computational and Data Sciences, College of Sciences, George Mason University, Fairfax, Virginia, USA John Wiley & Sons, Ltd c

2 CONTENTS FOREWORD TO THE SECOND EDITION ACKNOWLEDGEMENTS xiv xvii 1 INTRODUCTION AND GENERAL CONSIDERATIONS The CFD code Porting research codes to an industrial context Scope of the book 5 2 DATA STRUCTURES AND ALGORITHMS Representation of a grid Derived data structures for static data Elements surrounding points - linked lists Points surrounding points Elements surrounding elements Edges External faces Edges of an dement Derived data structures for dynamic data N-trees Sorting and searching Heap lists Proximity in space Bins Binary trees Quadtrees and octrees Nearest-neighbours and graphs Distance to surface 30 3 GRID GENERATION Description of the domain to be gridded Analytical functions Discretedata Variation of dement size and shape Internal measures of grid quality Analytical functions ^ Boxes ) 39

3 CONTENTS Point/line/surface sources Background grids Element size attached to CAD data Adaptive background grids Surface gridding with adaptive background grids Element type Automatic grid generation methods Other grid generation methods The advancing front technique Checking the intersection of faces Data structures to minimize search overheads Additional techniques to increase speed Additional techniques to enhance reliability Delaunay triangulation Circumsphere calculations Data structures to minimize search overheads Boundary recovery Additional techniques to increase speed Additional techniques to enhance reliability and quality Grid improvement Removal of bad elements Laplacian smoothing Grid optimization Selective mesh movement Diagonal swapping Optimal space-filling tetrahedra Grids with uniform cores Volume-to-surface meshing Navier-Stokes gridding techniques Design criteria for RANS gridders Smoothing of surface normals Point distribution along normals Subdivision of prisms into tetrahedra Element removal criteria Filling space with points/arbitrary objects The advancing front space-filling algorithm Point/object placement stencils Boundary consistency checks Maximum compaction techniques Arbitrary objects Deposition patterns Applications Space Shuttle ascend configuration PilotejectingfromF Circleof Willis Generic submarine body 105

4 Vll Ahmed carbody Track PointcloudforF Hopper füled with beans/ellipsoids Cube Med with spheres of different sizes APPROXIMATION THEORY The basic problem Point fitting Weighted residual methods Least-squares formulation Choice of trial functions Constant trial functions in one dimension Linear trial functions in one dimension Quadratic trial functions in one dimension Linear trial functions in two dimensions Quadratic trial functions in two dimensions General properties of shape functions Weighted residual methods with local functions Accuracy and effort Grid estimates APPROXIMATION OF OPERATORS Taxonomy of methods Finite difference methods Finite volume methods Galerkin finite dement methods Petrov-Galerkin finite dement methods Spectral dement methods The Poisson Operator Minimization problem An example Tutorial: code fragment for heat equation Recovery of derivatives First derivatives Second derivatives Higher derivatives DISCRETIZATION IN TIME Explicit schemes Implicit schemes Situations where implicit schemes pay off A word of caution 136

5 Vlll CONTENTS 7 SOLUTION OF LARGE SYSTEMS OF EQUATIONS Direct solvers Gaussian elimination Crout elimination Cholesky elimination Iterative solvers Matrix preconditioning Globalization procedures Multigrid methods The multigrid concept Injection and projection Operators Gridcycling Algorithmic complexity and storage requirements Smoothing An example SIMPLE EULER/NAVIER-STOKES SOLVERS Galerkin approximation Equivalency with FVM Lax-Wendroff(Taylor-Galerkin) Expediting the RHS evaluation Linear elements (triangles, tetrahedra) Solving for the consistent mass matrix Artificial viscosities Boundary conditions Viscous fluxes FLUX-CORRECTED TRANSPORT SCHEMES Algorithmic implementation The limiting procedure Steepening FCT for Taylor-Galerkin schemes Iterative limiting Limiting for Systems of equations Limiting any set of quantities Examples Shocktube Shock diffraction over a wall Summary EDGE-BASED COMPRESSIBLE FLOW SOLVERS The Laplacian Operator First derivatives: first form First derivatives: second form Edge-based schemes for advection-dominated PDEs Exact Riemann solver (Godunov scheme) Approximate Riemann solvers 195

6 IX Scalar limited dissipation Scalar dissipation with pressure sensors Scalar dissipation without gradients Taylor-Galerkin schemes Flux-corrected transport schemes INCOMPRESSIBLE FLOW SOLVERS The advection Operator Integration along characteristics Taylor-Galerkin Edge-based upwinding The divergence Operator Artificial compressibility Temporal discretization: projection schemes Temporal discretization: implicit schemes Temporal discretization of higher order Acceleration to the steady State Local timestepping Reduced pressure iterations Substepping for the advection terms Implicit treatment of the advection terms Projective predictionof pressure increments Examples von Karman vortex street NACA0012wing LPD-17topside flow study DARPA SUBOFF model Generic submarine forebody vortex flow study MESH MOVEMENT The ALE frame of reference Boundary conditions Geometrie conservation law Mesh movement algorithms Smoothingofthevelocityfield Smoothing of the coordinates Prescription via analytic funetions Region of moving elements PDE-based distance funetions Eikonal equation Laplace equation Penalization of deformed elements Special movement techniques for RANS grids Rotating parts/domains 240

7 X CONTENTS 12.9 Applications Multiple spheres PilotejectionfromF Drifting fleet of ships INTERPOLATION Basic Interpolation algorithm Fastest 1-time algorithm: brüte force Fastest iv-time algorithm: octree search Fastest known vicinity algorithm: neighbour-to-neighbour Fastest grid-to-grid algorithm: advancing-front vicinity Layering of brute-force searches Inside-out interpolation Measuring concavity Vectorization Conservative interpolation Conservative and monotonic interpolation Surface-grid-to-surface-grid interpolation Particle-grid interpolation ADAPTIVE MESH REFINEMENT Optimal-mesh criteria Error indicators/estimators Error indicators commonly used Problems with multiple scales Determination of element size and shape Refinement strategies Mesh movement or repositioning (r-methods) Mesh enrichment (h/p-methods) Adaptive remeshing (M-methods) Combinations Tutorial: h-refinement with tetrahedra Algorithmic implementation Examples Convection between concentric cylinders Shock-object interaction in two dimensions Shock-object interaction in three dimensions Shock-structure interaction Object falling into supersonic free stream two dimensions EFFICIENT USE OF COMPUTER HARDWARE Reduction of cache-misses Array access in loops Point renumbering Reordering of nodes within elements Renumbering of edges according to points 306

8 CONTENTS xi Some timings Agglomeration techniques Vector machines Basic edge colouring algorithm Backward/forward strategy Combining vectorizability with data locality Switching algorithm Reduced i/a loops Alternative RHS formation Parallel machines: general considerations Shared-memory parallel machines Local agglomeration Global agglomeration Implementational issues SIMD machines MIMD machines General considerations Load balancing and domain Splitting Parallel flow solvers The effect ofmoore's law on parallel Computing The life cycle of scientific Computing codes Examples The consequences ofmoore's law SPACE-MARCHING AND DEACTIVATION Space-marching Masking of points and edges Renumbering of points and edges Grouping to avoid memory contention Extrapolation of the Solution Treatment of subsonic pockets Measuring convergence Application to transient problems Macro-blocking Examples for space-marching and blocking Deactivation Examples of dynamic deactivation OVERLAPPING GRIDS Interpolation criteria External boundaries and domains Interpolation: initialization Treatment of domains that are partially outside Removal of inactive regions Incremental interpolation Changes to the flow solver 377

9 XÜ CONTENTS 17.8 Examples Sphere in Channel (compressible Euler) Sphere in shear flow (incompressible Navier-Stokes) Spinning missile EMBEDDED AND IMMERSED GRID TECHNIQUES Kinetic treatment of embedded or immersed objects Implementation details Kinematic treatment of embedded surfaces First-order treatment Higher-order treatment Determination of crossed edges Deactivation of interior regions Extrapolation of the Solution Adaptive mesh refinement Load/flux transfer Treatment of gaps or cracks Direct link to particles Examples Sodshocktube Shuttle ascend configuration Blast interaction with a generic ship hüll Generic weapon fragmentation Flow past a sphere Dispersion in an inner city Complex endovascular devices Flow past a VW Golf TREATMENT OF FREE SURFACES Interface fitting methods Free surface discretization Overall scheme Mesh update Examples for surface fitting Practical limitations of free surface fitting Interface capturing methods Extrapolation of the pressure Extrapolation of the velocity Keeping interfaces sharp Imposition of constant mass Deactivation of air region Treatment ofbubbles Adaptive refinement Examples for surface capturing Practical limitations of free surface capturing 448

10 CONTENTS XÜi 20 OPTIMAL SHAPE AND PROCESS DESIGN The general optimization problem Optimization techniques Recursive exhaustive parameter scoping Genetic algorithms Gradient-based algorithms Adjoint solvers Adjoint equations: residuals with first derivatives and source terms Adjoint equations: residuals with second derivatives Jacobians for Euler/Navier-Stokes equations Adjoint solvers Gradient evaluation Geometrie constraints Volume constraint via cost funetion Volume constraint via gradient projeetion Volume constraint via post-processing Approximate gradients Multipoint optimization Representation of surface changes Hierarchical design procedures Topological optimization via porosities Examples Damage assessment for contaminant release External nozzle Wigley hüll KRISO Container ship(kcs) 480 References 481 Index 515