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Preface	p. v
Introduction	p. xi
Constructive Modeling of Free Developed Turbulence - Coherent Structures, Laminar-Turbulent Transition, Chaos	p. 1
Introduction	p. 1
Rational averaging of large vortex structures	p. 12
Some experimental and theoretical investigations	p. 29
General problem formulation	p. 38
Simulation of coherent structures in turbulent flows	p. 41
Correctness of the problem formulation	p. 50
Calculated results for coherent structures in the wake behind a body	p. 53
On the analysis of spectral characteristics	p. 60
Numerical simulation of the random component of turbulence	p. 71
Laminar-turbulent transition. Simulation of three-dimensional flows in clean rooms	p. 76
Transition to chaos (numerical experiments)	p. 84
General aspects	p. 84
"Kolmogoroff's flow" of the viscous fluid at subcritical and supercritical regimes. Transition to chaos	p. 86
Study of the large-scale turbulence in ocean	p. 111
Numerical simulation of the internal waves in a stratified fluid	p. 128
Rayleigh-Taylor instability: evolution to the turbulent stage	p. 137
Numerical simulation of the convective flow over large-scale source of energy (big fire in the atmosphere)	p. 143
Axiomatic model of fully developed turbulence	p. 152
Conclusion	p. 154
Acknowledgement	p. 157
References	p. 157
Modeling of Richtmyer-Meshkov Instability	p. 164
Introduction	p. 164
Numerical method	p. 169
Model calculations	p. 171
The Couchy problem for one-dimensional isotopic flow of an ideal gas	p. 174
Boundary conditions	p. 176
Comparison of results by different models	p. 178
The analytical approach	p. 181
Computational experiment	p. 186
Physical mechanisms of the RMI evolution	p. 190
A sequential transition to turbulence in RMI instability	p. 198
Three-dimensional numerical simulation of the RMI	p. 200
Conclusion	p. 208
Appendix	p. 209
References	p. 210
Rayleigh-Taylor Instability: Analysis and Numerical Simulation	p. 214
The theory of Rayleigh-Taylor instability: modulatory perturbations and mushroom-flow dynamics	p. 214
Introduction	p. 214
Periodicity and symmetry of modulatory perturbations	p. 216
Cutting off the singularities associated with jets	p. 220
Classification of perturbations	p. 223
Results	p. 227
Classification of stability problems	p. 230
Initiation of a mushroom structure	p. 232
The mushroom flow structure	p. 238
Numerical simulation	p. 243
Development of the Rayleigh-Taylor instability: numerical simulations	p. 246
Introduction	p. 246
Numerical simulation of RTI development by the method of large particles	p. 247
Intermode interaction in RTI	p. 252
RTI simulation by the method of pseudo-compressibility	p. 257
Numerical simulation of the RTI development by means of high-resolution Euler hydrocode	p. 262
References	p. 280
Direct Statistical Approach for Aerohydrodynamic Problems	p. 285
Statistical modeling in rarefied gas-dynamics	p. 285
Introduction	p. 285
Stochastic analogue of the Boltzmann equation	p. 287
Probabilistic approach to the basic equation of the collision stage	p. 291
Algorithms for modeling the collision relaxation	p. 294
Direct statistical modeling of the shock wave in gaseous flow with velocity pulsations	p. 299
Introduction	p. 299
Problem formulation	p. 300
Results of the numerical modeling	p. 303
Conclusion	p. 307
Direct statistical simulation for some problems of turbulence	p. 307
Introduction	p. 307
An application of the statistical method of particles in cell for simulation of the momentumless wake	p. 308
An application of the statistical method of particles in cell to the problem of a turbulent spot	p. 311
The direct statistical modeling of the turbulence within a wake behind the cylinder	p. 320
Simulation results	p. 330
Conclusion	p. 331
References	p. 333
Computational Experiment: Direct Numerical Simulation of Complex Gas-Dynamical Flows on the Basis of Euler, Navier-Stokes, and Boltzmann Models	p. 336
Introduction	p. 336
The use of numerical methods	p. 336
Numerical methods applicable to gas-dynamical problems	p. 339
Method of finite differences	p. 340
Method of integral relations	p. 340
Method of characteristics	p. 341
Particle-in-cell (PIC) method	p. 341
Development of numerical algorithms	p. 342
Steady-state schemes	p. 342
Unsteady-state schemes	p. 344
Large-particle method	p. 344
Computational experiments	p. 345
"Large-particles" method for the study of complex gas flows	p. 347
Calculations	p. 347
Boundary conditions	p. 349
Viscosity effects	p. 350
Stability of the scheme	p. 352
Advantages	p. 354
Results	p. 355
Computation of incompressible viscous flows	p. 363
The problem	p. 363
The difference scheme	p. 364
Results	p. 367
Computation of viscous compressible gas flow (conservative flow method)	p. 369
The method	p. 369
Analysis	p. 372
Results	p. 374
Statistical model for the investigation of rarefied gas flows	p. 376
The model	p. 376
The method	p. 378
Results	p. 383
Conclusion	p. 386
References	p. 386
Formation of Large-Scale Structures in the Gap Between Rotating Cylinders: the Rayleigh-Zeldovich Problem	p. 389
Introduction	p. 389
Background	p. 391
Direct numerical simulation methodology	p. 392
Statement of the problem and results	p. 393
The inner cylinder is at rest and the outer cylinder is rotating	p. 394
The inner cylinder is at rest and the outer cylinder is brought to rest	p. 398
The inner cylinder is rotating and the outer cylinder is at rest	p. 400
Conclusions	p. 403
References	p. 404
Universal Technology of Parallel Computations for the Problems Described by Systems of the Equations of Hyperbolic Type: A Step to Supersolver	p. 405
Introduction	p. 405
Unified methodics	p. 406
A method for using non-conservative variables	p. 410
Parallel program implementation	p. 413
Results of numerical simulation	p. 415
Conclusion	p. 418
References	p. 420
Supercomputers in Mathematical Modeling of the High Complexity Problems	p. 422
Introduction	p. 422
Turbulence and hydrodynamic instabilities	p. 424
Supersolver	p. 428
Applications	p. 429
Gas-dynamics (CFD)	p. 429
Hydrodynamic instabilities	p. 434
Seismic data processing	p. 436
Safety of housing and industrial constructions under intensive dynamic loadings	p. 437
Nonlinear contact shell dynamics	p. 439
Computer models in medicine	p. 440
Conclusion	p. 444
References	p. 445
On Nuts and Bolts of Structural Turbulence and Hydrodynamic Instabilities	p. 448
Rational Constructivism	p. 448
Back in Mechanics	p. 449
Large Vortices	p. 450
Structural Instabilities	p. 452
Vortex Cascades	p. 453
Principal Modes	p. 453
References	p. 456
List of the Main Publications of	p. 459
Monographs	p. 459
Papers	p. 460
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Constructive Modeling Of Structural Turbulence And Hydrodynamic Instabilities

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Constructive Modeling Of Structural Turbulence And Hydrodynamic Instabilities

9789812833013

9812833013

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