ISBN: 3-540-65433-X
TITLE: Efficient Solvers for Incompressible Flow Problems
AUTHOR: Turek, Stefan
TOC:

Notation XIII
1 Motivation for current research 1
1.1 Results and conclusions from Benchmark calculations 4
1.2 Numerical and algorithmic bottlenecks of CFD tools 16
2 Derivation of NavierStokes solvers 27
2.1 Mathematical description of NavierStokes solvers 32
2.2 The general "Pressure Schur Complement" approach 38
2.3 "Global Multilevel Pressure Schur Complement" 46
2.3.1 The "reactive" preconditioner A_R 48
2.3.2 The "diffusive" preconditioner A_D 54
2.3.3 The "convective" preconditioner A_K 56
2.3.4 The "factorized" preconditioner 59
2.4 "Local Multilevel Pressure Schur Complement" 67
2.4.1 The local "Pressure Schur Complement" preconditioner 67
2.4.2 Blocking strategies for building patches Omega_i 72
2.5 Resulting schemes and relation to other existing methods 78
3 Other mathematical components 97
3.1 Finite element spaces 98
3.1.1 Criterions for the comparison of various Stokes elements 101
3.1.2 Some properties of the nonconforming rotated multilinear spaces 107
3.1.3 The discretely divergencefree subspaces 115
3.1.4 Stabilization techniques for convective terms 124
3.1.5 A posteriori error control mechanisms for finite element approaches 147
3.2 Time stepping techniques 161
3.2.1 The Fractionalsteptheta scheme and other Onesteptheta schemes 162
3.2.2 Numerical comparisons of some time discretization schemes 168
3.2.3 Adaptive time stepping for incompressible flow problems 174
3.3 Nonlinear iteration techniques 178
3.3.1 The "adaptive fixed point defect correction" method 181
3.3.2 Numerical aspects of nonlinear (and linear) iteration schemes 189
3.3.3 Linearization techniques for nonstationary flows 203
3.3.4 Other nonlinear techniques for the NavierStokes equations 206
3.4 Linear multigrid techniques 208
3.4.1 Linear basic iterations and their properties as smoothers 212
3.4.2 Grid transfer, coarse grid operators and control of correction 218
3.4.3 Numerical examples for multigrid performance 227
3.5 Boundary conditions 247
3.5.1 Variational formulations in unbounded domains 249
3.5.2 Variational formulations in bounded domains 253
3.5.3 Associated boundary conditions of flux and pressure drop type 266
3.5.4 Implementation of boundary conditions 269
4 Numerical comparisons of Navier-Stokes solvers 281
4.1 Some exemplary numerical examples 285
4.2 Conclusions from the numerical simulations 325
5 Conclusions and outlook 335
6 The enclosed CDROM 341
Bibliography 343
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