ALBERT

Description / Table of Contents: Table of Contents: Preface and Acknowledgments. - 1 Introductory comments and summary. - 1.1 Introduction. - 1.2 Summary of the chapters. - 1.3 Conclusions. - 2 Finite differences. - 2.1 Introduction. - 2.2 Difference operators. - 2.2.1 Space discretization. - 2.2.2 Non-uniform grids. - 2.2.3 Coordinate transformations. - 2.2.3a Two walls clustering. - 2.2.3b Uniform in the center, stretched in the far field. - 2.2.3c Clustered in the center. - 2.2.3d Clustered around two inner regions. - 2.2.3e Clustered near two walls and at the center. - 2.2.3f Clustered in one region and stretched elsewhere. - 2.2.4 Non-uniform grids boundary conditions. - 2.3 Parabolic equations intime. - 2.3.1 Crank-Nicholson implicit scheme. - 2.3.2 Adams-Bashfort explicit. - 2.3.3 Low storage third-order Runge-Kutta Explicit. - 2.3.4 Hybrid third-order Runge-Kutta/Crank-Nicholson. - 2.3.5 Third order Runge-Kutta vs Adams-Bashfort. - 2.4. FFT for elliptic partial differential equations. - 2.4.1 Solution by FFT. - 2.4.2 Two periodic directions. - 2.4.3 sinFFT. - 2.4.4 cosFFT centered. - 2.4.5 cosFFT "staggered". - 2.5 Multigrid methods for elliptic partial differential equations. - 2.5.1 Multigrid method. - 2.6 Conclusions. - 3 The Burgers equation. - 3.1 Physical considerations. - 3.2 Spatial discretization. - 3.3 Time discretization. - 3.4 Results. - 3.5 Conclusions. - 4 Two-dimensional flows in Cartesian coordinates. - 4.1. Introduction. - 4.2 The equations in vorticity-streamfunction formulation. - 4.3 Vorticity boundary conditions. - 4.3a Periodicity. - 4.3b Free-slip. - 4.3c No-slip. - 4.3d Outlet. - 4.4 Streamfunction boundary conditions. - 4.5 Physical aspects of nonlinear terms. - 4.6 Arakawa's scheme. - 4.7 Nonlinear terms in primitive variables. - 4.8. Viscous terms and factorization. - 4.9 Boundary conditions. - 4.10 Test of [Omega, Psi] formulation. - 4.11 Code PSOMGBC. - 4.11a Input data. - 4.11b Initial conditions. - 4.11b.a Lamb dipole. - 4.11b.b Stern dipole. - 4.11b.c Isolated vortex. - 4.11b.d Monopole in a [Beta] plane. - 4.11b.e Flow near a coast with topography slopes. - 4.11b.f Time developing mixing layer. - 4.11b.g Space developing mixing layer. - 4.12 Results by the code PSOMGBC. - 4.12.1 General suggestion. - 4.12.2 Flow phenomena simulations. - 4.12.2a Lamb dipoles. - 4.12.2b Modons. - 4.12.2c Tripoles. - 4.12.2d Monopols in a [Beta] plane. - 4.12.2e Flow over topographic slopes. - 4.12.2f Time developing mixing layers. - 4.12.2g Roll-up. - 4.12.2h The pairing. - 4.12.2i Arakawa scheme effects. - 4.12.2j Space developing mixing layers. - 4.13 Conclusions. - 5 Two-dimensional flows in general curvilinear coordinates. - 5.1 Introduction. - 5.2 Equations. - 5.3 Laplacian discretization. - 5.4 Nonlinear terms discretization. - 5.5 Boundary conditions. - 5.6 Time discretization. - 5.7Code PSOMCUR. - 5.8 Results. - 5.8a Inviscid dipole moving close to a bump. - 5.8b Dipole impinging a semicircular cavity. - 5.8c Stream around a Gaussian hill. - 5.9 Conclusions. - 6 Two-dimensional turbulence. - 6.1. Introduction. - 6.2 Arakawa fourth order scheme. - 6.3 Initial conditions. - 6.4 Code TURB2D. - 6.5 Results. - 6.5.1 Resolution check. - 6.5.2 Global conservation properties. - 6.6 Conclusions. - 7 Axisymmetric flows. - 7.1 Introduction. - 7.2 Equations for the vorticity formulation. - 7.3 Results. - 7.3a Vortex ring formation. - 7.3b Vortex ring in the presence of solid body rotation. - 7.3c Vortex rings impacting free-slip walls. - 7.3d Vortex rings impacting no-slip walls. - 7.3e Space developing coaxial jet. - 7.4 Conclusions. - 8 Three-dimensional flows with three periodic directions. - 8.1 Introduction. - 8.2 Governing equations. - 8.3 Space and time discretization. - 8.4 Discretization of the non-linear terms. - 8.5 Fractional step. - 8.6 Factorization in the [Ypsilon]i equations. - 8.7 Solution of the Poisson equation for [Phi]. - 8.8 Initial conditions. - 8.8.1 Isotropic turbulence. - 8.8.2 Lamb dipole stability. - 8.9 Numerical checks of the code ISO. - 8.10 Definition of turbulent quantities. - 8.11 Isotropic turbulence with and without rotation. - 8.11a Isotropic turbulence. - 8.11b Isotropic turbulence subjected to uniform rotation. - 8.12 Physics of turbulence from data. - 8.12.a Correlation tensor. - 8.12.b Probability Density Functions. - 8.12.b.1 PDF of velocity and vorticity components. - 8.12.b.2 PDF of pressure field. - 8.12.b.3 PDF of angle between velocity and vorticity vectors. - 8.12.b.4 Velocity structure functions. - 8.13 Stability of the Lamb dipole to three dimensional disturbances. - 8.14 Conclusions. - 9 Flows with walls in Cartesian coordinates. - 9.1 Introduction. - 9.2 Adimensionalization. - 9.3 Space and time discretization. - 9.4 Initial conditions. - 9.5 Wall boundaries for turbulence control. - 9.6 Definition of turbulent quantities. - 9.7 Check of the code CHADS. - 9.8 Wall-boundary conditions effects. - 9.9 Analysis of the data. - 9.9a Velocity statistics. - 9.9b Vorticity statistics. - 9.9c Production and dissipation rate. - 9.9d Velocity vorticity tensor. - 9.9e Velocity vorticity spectra. - 9.9f Velocity and vorticity cospectra. - 9.9g Velocity and vorticity two-point correlations. - 9.9h Joint PDF of velocity and vorticity correlations in one point. - 9.9i Vortex stretching. - 9.9j Budget in the one-point closure equations. - 9.10 Conclusions. - 10 Flows in cylindrical coordinates with one wall. - 10.1 Introduction. - 10.2 Governing equations. - 10.3. Numerical method. - 10.4. Treatment of the axis. - 10.5 Code informations. - 10.5a Calculation of qi (first step). - 10.5b Calculation of qi n+1 (second step). - 10.5c Initial conditions. - 10.6 Results. - 10.6a Check of axis accuracy. - 10.6b Check of energy conservation. - 10.6c Turbulent non-rotating pipe, coarse solution. - 10.6b Turbulent rotating pipe, coarse solution. - 10.7 Conclusions. - 11 Flows in cylindrical coordinates with two walls. - 11.1 Introduction. - 11.2 Governing equations and numerical model. - 11.3 Code general informations. - 11.3a Description of the file tr3dnuma.f. - 11.3b Description of the file fr3dnuge.f. - 11.3c Description of the file tr3dnucoJ. - 11.3d Description of the file tr3dnuintr.f. - 11.3e Description of the file tr3dnuinri.f. - 11.3f Description of the file tr3dnuhnJ. - 11.3g Description of the file tr3dnutnJ. - 11.3h Description of the file tr3dnutr.f. - 11.3i Description of the file tr3dnutu.f. - 11.3j Description of the file tr3dnuioJ. - 11.4 Results. - 11.4a Three-dimensional tripole formation. - 11.4b Three-dimensional impact of a vortex ring on a wall. - 11.5 Conclusions. - 12 Large eddy simulations. - 12.1. Introduction. - 12.2. Filtering. - 12.3. Equations. - 12.4. Subgrid models. - 12.4a Smagorinsky model for the residual stress. - 12.4b Structure function model. - 12.4c Dynamic subgrid model. - 12.4d Similarity scale models. - 12.5 Equations for density-Related problems. - 12.6 Subgrid model for the rmal flows. - 12.7 Code informations. - 12.7a Description of the file isolesma.f. - 2.7b Description of the file isolesnn.f. - 12.7c Description of the file isoleshn.f. - 12.7d Description of the file isolestn.f. - 12.7e Description of the file isolestnsi.f. - 12.7f Description of the file isolesintu.f . - 12.7g Description of the file isolesinsi.f. - 12.7h Description of the file isolesph.f. - 12.7i Description of the file isolessp.f. - 12.7j Description of the file isolesst.f. - 12.7k Description of the file isolestr.f. - 12.71 Description of the file isolesio.f. - 12.7m Description of the file isolesiosi.f. - 12.7n Subgrid-models. - 12.8 Results. - 12.8a Grid turbulence at intermediate R [Lambda]. - 12.8b Isotropic turbulence at high R [Lambda]. - 12.8c Isotropic turbulence with a passive scalar. - 12.8d Buoyancy-generated turbulence. - 12.8e Turbulence with buoyancy and stratification. - 12.9 Conclusions. - 13 Large eddy simulations of wall-bounded flows. - 13.1. Introduction. - 13.2. Equations. - 13.3. Results. - 13.3.a Results at low Reynolds number. - 13.3.a Results at high Reynolds numbers. - 13.4 Conclusions. - References. - Diskette information. - Plates section.

Description / Table of Contents: This book deals with the simulation of the incompressible Navier-Stokes equations for laminar and turbulent flows. The book is limited to explaining and employing the finite difference method. This book furnishes a large number of source codes which permit to play with the Navier-Stokes equations and to understand the complex physics related to fluid mechanics. Numerical simulations are useful tools to understand the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transfering one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory. Two chapters on Large Eddy Simulations (LES) habe been included since it is a methodology that in the near future will allow having more universal turbulence models for practical applications. The direct simulation of the Navier-Stokes equations (DNS) is simple by finite-differences, that are satisfactory to reproduce the dynamics of turbulent flows. A large part of the book is devoted to study homogeneous and wall turbulent flows. In the second chapter the elementary concept of finite difference is given to solve parabolic and elliptical partial differential equations. In successive chapters the 1D, 2D, and 3D Navier-Stokes equations are solved in Cartesian and cylindrical coordinates. Finally, Large Eddy Simulations are performed to check the importance of the subgrid scale models. Results for turbulent and laminar flows are discussed with particular emphasis on vortex dynamics. This volume will be of interest to graduate students and researchers wanting to compare experiments and numerical simulations, and to workers in the mechanical and aeronautic industries.