Computational Fluid Dynamics

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ISBN: 9781439856611 | 1439856613
Cover: Hardcover
Copyright: 8/24/2011

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This reference concentrates on advanced techniques of computational fluid dynamics. It offers illustrations of new developments of classical methods as well as recent methods that appear in the field. Each chapter takes a tutorial approach and covers a different method or application. Topics discussed include finite volumes, weighted residuals, spectral methods, smoothed-particle hydrodynamics (SPH), application of SPH methods to conservation equations, finite volume particle methods (FVPM), and numerical algorithms for unstructured meshes. The authors offer theory, algorithms, and applications for each topic.

List of figures	p. xiii
List of tables	p. xxiii
Preface	p. xxv
Warranty	p. xxxi
Finite volume methods	p. 1
Introduction	p. 1
Conservativity	p. 2
Control volume integration	p. 4
Grid	p. 6
General flux interpolation	p. 7
Resolution and time discretization	p. 8
Unsteady resolution	p. 9
Steady resolution	p. 10
Consistency, stability, and convergence	p. 13
Upwind interpolation	p. 16
Steger-Warming approach	p. 17
Roe scheme: approximate Riemann solver	p. 18
Particular case of structured grids	p. 19
Flux interpolation on regular grids	p. 20
Curvilinear grids	p. 21
Boundary conditions	p. 23
Weighted residuals methods	p. 25
Introduction	p. 25
Principles of the weighted residuals method	p. 27
Collocation or pseudo-spectral method	p. 28
Least squares method	p. 29
Method of moments	p. 29
Galerkin approximation	p. 30
Subdomains	p. 30
An example	p. 30
Spectral methods	p. 33
Introduction	p. 33
Linear problem: Galerkin, tau, and collocation methods	p. 33
Galerkin approximation	p. 35
Tau method	p. 37
Collocation method	p. 37
Applications: Fourier	p. 38
Fourier Galerkin approximation for the Burgers equation	p. 38
Fourier collocation for Burgers' equation	p. 40
Applications: Chebyshev	p. 41
Computation of derivatives	p. 41
Chebyshev tau approximation for Burgers' equation	p. 43
Chebyshev collocation	p. 45
Implicit equations	p. 46
Fourier approximation	p. 46
Chebyshev tau approximation	p. 47
Evaluation of nonlinear terms	p. 51
Problem of aliasing	p. 52
Convolution sums	p. 54
Numerical evaluation by a pseudo-spectral transformation method	p. 54
De-aliasing by the 3/2 rule	p. 55
De-aliasing by phase-shifting	p. 56
Errors and convergence	p. 56
Wavenumber, vortex, wavelet	p. 58
Smoothed-particle hydrodynamics (SPH) methods	p. 63
Introduction	p. 63
SPH approximation of a function	p. 64
Properties of the kernel function W	p. 66
Barycenter of D(x_i)	p. 67
Choices of the kernel function W	p. 68
SPH approximation of differential operators applied on a function ¿	p. 69
Basic formulation	p. 69
Consistent formulation for a constant function or global conservation	p. 70
The use of an adjoint operator of ∇¿	p. 71
Consistent formulation for a linear function - Renormalization	p. 73
Derivatives with a Shepard's kernel ¿	p. 79
Using a Taylor series expansion	p. 82
Concluding remarks	p. 84
Application of SPH methods to conservation equations	p. 87
General form of conservation equations	p. 87
Weak SPH-ALE formulation of the conservation equations	p. 88
SPH approximation of conservation equations	p. 88
Improved SPH approximation accurate to second order	p. 90
Global conservation of transported quantities ¿	p. 91
Numerical viscosity	p. 91
Godunov's scheme and Riemann solver	p. 93
The analogy with finite volume method	p. 93
Riemann solver	p. 95
Numerical viscosity and Riemann solver	p. 96
Application to flow conservation equations	p. 97
Euler equation for a non-viscous fluid	p. 97
Practical implementation of Riemann solver in an SPH method	p. 98
Boundary conditions	p. 100
Boundary repulsive forces	p. 100
Mirror particles	p. 101
Ghost particles	p. 102
Normalizing conditions	p. 106
The semi-analytical method	p. 107
SPH-ALE boundary treatment	p. 109
Applications of SPH and SPH-ALE methods	p. 112
Flow in a single steady Pelton bucket	p. 113
Flows in a rotating Pelton runner	p. 116
Finite volume particle methods (FVPM)	p. 119
Introduction	p. 119
Partition of unity	p. 120
Average of a function ¿	p. 121
Derivatives of ¿	p. 122
Lagrangian derivative of ¿	p. 122
Other useful coefficients and "closed box" condition	p. 123
Transport of the volume V_i	p. 125
On the computation of the gradient ∇¿_i	p. 125
Method of Nestor	p. 125
Method of Keck	p. 126
Conservation equation and FVPM	p. 126
Concluding remarks	p. 129
Numerical algorithms for unstructured meshes	p. 131
Introduction	p. 131
Spatial representation	p. 134
A particular P1 finite-element Galerkin formulation	p. 134
Mixed-element-volume basic equivalence	p. 136
Circumcenter cells	p. 139
Flux integration	p. 141
Towards higher spatial order	p. 143
The MUSCL method	p. 143
Low dissipation advection schemes: 1D	p. 145
Unstructured two-dimensional case	p. 149
Extension to Euler: NLV6	p. 150
High-order LV6 spatial scheme	p. 151
Time advancing	p. 152
Conclusion on super convergent schemes	p. 153
Positivity of mixed element-volume formulations	p. 154
Introduction	p. 154
Positive schemes and LED schemes for nonlinear scalar conservation laws	p. 154
Density-positive MEV schemes for the Euler equations	p. 165
A numerical example	p. 171
Conclusion for positiveness	p. 174
3D multi-scales anisotropic mesh adaptation	p. 175
Anisotropic mesh generation	p. 176
Continuous mesh model and optimality	p. 177
Application to numerical computation	p. 179
Application to a supersonic business jet	p. 180
3D goal-oriented anisotropic mesh adaptation	p. 182
Introduction	p. 182
A more accurate nonlinear error analysis	p. 186
The case of the steady Euler equations	p. 189
Error model minimization	p. 190
Adaptive strategy	p. 192
Some examples	p. 194
Concluding remarks	p. 202
LES, variations! multiscale LES, and hybrid models	p. 205
Introduction	p. 206
Numerical model	p. 211
Navier-Stokes equations	p. 211
Discretization of hyperbolic fluxes	p. 212
Time advancing	p. 214
Large eddy simulation (LES)	p. 215
Smagorinsky and dynamic models	p. 215
Comparison of Smagorinsky and dynamic LES models	p. 217
WALE and Vreman's models	p. 230
Variational multiscale large eddy simulation (VMS-LES)	p. 231
Model features and description	p. 231
The impact of VMS-LES vs. LES	p. 236
Hybrid RANS/LES	p. 249
Model features and description	p. 249
Detached eddy simulation	p. 249
Limited numerical scales (LNS) approach	p. 250
A second-generation hybrid model	p. 251
The interest in hybridizing RANS and VMS-LES	p. 255
Concluding remarks	p. 258
Numerical algorithms for free surface flow	p. 263
Introduction	p. 263
A short review on two-phases flow with free surfaces	p. 265
Incompressible and compressible media	p. 266
Eulerian vs. Lagrangian techniques	p. 267
Lagrangian methods	p. 267
Arbitrary Lagrangian Eulerian (ALE) methods	p. 269
Particles methods	p. 270
Immersed boundary methods	p. 271
Level sets methods	p. 272
Volume-of-fluid methods	p. 275
Some preliminary remarks on ice and glacier modeling	p. 277
Modeling	p. 279
Modeling of liquid flow	p. 279
Modeling of ice flow	p. 281
Time splitting scheme	p. 286
Liquid flow	p. 286
Ice flow	p. 288
A two-grids method for space discretization	p. 290
Liquid flow	p. 290
Ice flow	p. 297
Modeling of interfacial effects	p. 301
Modeling of gas pressure	p. 302
Modeling of surface tension	p. 304
Numerical results for liquid flow	p. 305
Casting problems	p. 306
Sloshing simulations	p. 307
Bubbles simulations with surface tension	p. 307
Numerical results for ice flow	p. 310
Muragl glacier	p. 310
Rhone glacier	p. 314
Concluding remarks	p. 322
Acknowledgments	p. 327
Bibliography	p. 329
Editor Biography	p. 369
List of Contributors	p. 371
Index	p. 372
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Computational Fluid Dynamics

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