Turbulent flow computation Machine generated contents note: Preface vii Contributing Authors xi 1 Under Resolution and Diagnostics in Spectral Simulations of Complex 1 Geometry Flows Robert M. Kirby and George Em Karniadakis 1 Introduction 1 2 Spectral Methods on Unstructured Grids 6 3 Nonlinearities and Dealiasing 15 4 Under Resolution and Diagnostics 21 5 Discussion 36 2 High Resolution Methods for Computing Turbulent Flows 43 William J. Rider and Dimitris Drikakis 1 Motivation 43 2 Multimaterial Mixing 44 3 Numerical Methods as LES Models 49 4 Theoretical Basis 54 5 Modified Equations for Limiters 56 6 Towards an Implicit Turbulence Model 62 7 Numerical Experiments: Burgers Equation 66 8 Closing Remarks 71 3 Preserving symmetry in convection diffusion schemes 75 R. WC. P Verstappen and A.E.P Veldman 1 Introduction 75 2 Symmetry preserving discretization 82 3 A test case: turbulent channel flow 93 4 Conclusions 98 4 Analysis and control of errors in the numerical simulation of turbulence 101 Sandip Ghosal 1 Introduction 101 2 Sources of Errors & Their Nature 102 3 Spectral Analysis of Errors 114 5 Designing Adaptive Low Dissipative High Order Schemes for Long time 141 Integrations H.C. Yee B. Sjdgreen 1 Introduction 142 2 Conditioning of the Governing Equations 143 3 Discrete Analogue of the Continuum 153 4 Adaptive Numerical Dissipation Control 157 5 High Order Filter Finite Difference Methods 160 6 Numerical Examples 175 7 Concluding Remarks 189 6 Building Blocks for Reliable Complex Nonlinear Numerical Simulations 199 H.C. Yee 1 Introduction 199 2 Sources of Nonlinearities and Knowledge Gained from Nonlinear Model Problems 202 3 Minimization of Spurious Steady State via Bifurcation Theory 204 4 Source Term Treatments in Reacting Flows 207 5 Adaptive Numerical Methods 208 6 Spurious Numerics Relevant to Turbulent Flow Computations 209 7 Alpha modeling strategy for LES of turbulent mixing 237 Bernard J. Geurts and Darryl D. Holm 1 Introduction 237 2 Large eddy simulation and a modeling 243 3 Numerical simulations of a turbulent mixing layer 257 4 LES a of a mixing layer 262 5 Concluding remarks 273 8 Forward in Time Differencing for Fluids: Simulation of geophysical turbulence 279 Piotr K. Smolarkiewicz and Joseph. M. Prusa 1 Introduction 279 2 NFT methods for fluids 285 3 Accuracy of NFT methods 289 4 VLES of global geophysical turbulence an example 296 5 Concluding remarks 306 9 Direct Numerical Simulations of Multiphase Flows 313 G. Tryggvason A. Ferndndez A. Esmaeeli and B. Bunner 1 Introduction 313 2 Formulation and Numerical Method 316 3 Results 321 4 Conclusions 333 10 Examples of Contemporary CFD Simulations 339 S.R. Chakravarthy U.C. Goldberg and P. Batten 1 Introduction 339 2 Flow Examples 347 3 Concluding remarks 365 This book presents a coherent account of contemporary computational approaches for turbulent flows. It aims to provide the reader with information about the current state of the art as well as to stimulate directions for future research and development. The book puts particular emphasis on computational methods for incompressible and compressible turbulent flows as well as on methods for analysing and quantifying numerical errors in turbulent flow computations. Apart from reviewing main research developments new previously unpublished material is also included in many of the chapters. This book aims to appeal to a broad audience of applied scientists and engineers who are involved in the development and application of computational fluid dynamics (CFD) methods for turbulent flows. The readership includes academic researchers as well as CFD practitioners in industry. The chapters were specifically composed to also constitute an advanced textbook for PhD candidates in the field of CFD and turbulence. The book can also be used as a textbook at the level of MSc or MEng studies in engineering physics and applied mathematics departments