Title:
Monte Carlo methods in mechanics of fluid and gas
Personal Author:
Publication Information:
Hackensack, N.J. : World Scientific, c2010.
Physical Description:
xii, 268 p. : ill. ; 24 cm.
ISBN:
9789814282352
Added Author:
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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010274638 | QC168.86 B46 2010 | Open Access Book | Book | Searching... |
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Summary
Summary
This book is devoted to analysis of Monte Carlo methods developed in rarefied gas dynamics. Presented is the short history of the development of such methods, described are their main properties, their advantages and deficiencies. It is shown that the contemporary stage in the progress of computational methods cannot be regarded without a complex approach to the preparation of algorithms taking into account all the peculiarities of the problem under consideration, that is, of the physical nature of a process, the mathematical model and the theoretical aspects of computational mathematics and stochastic processes. Thoroughly investigated is the possibility of application of Monte Carlo methods in some kindred areas of science which are non-traditional for the use of statistical modeling (continuous media, turbulence). Considered are the possible directions of development of statistical modeling.
Table of Contents
| Preface | p. v |
| 0 Introduction | p. 1 |
| 1 The Main Equations and Approaches to Solutions of the Problems in Rarefied Gas Dynamics | p. 23 |
| 1.1 The Main Equations in Rarefied Gas Dynamics | p. 23 |
| 1.2 The Main Approaches to the Construction of Statistical Algorithms | p. 25 |
| 1.3 Connection of the Stationary Modeling with the Solution of Equation | p. 26 |
| 1.4 Construction of the Method of Direct Statistical Modeling | p. 28 |
| 2 Development of the Numerical Methods of Solution of the Linear Kinetic Equations | p. 30 |
| 2.1 The Perfection of VGK Method (Vlasov, Gorelov, Kogan) | p. 30 |
| 2.2 Modification of the Vlasov's Method for the Solution of Linear Problems | p. 35 |
| 2.3 Method of Solution of the Linearized Boltzmann's Equation | p. 38 |
| 3 Methods of Solution of the Nonlinear Problems in Rarefied Gas Dynamics | p. 43 |
| 3.1 Method of Solution of the Model Equation Based on a Stationary Modeling | p. 43 |
| 3.2 The Possibilities of the Scheme of Splitting for the Solution of Kinetic Equations | p. 46 |
| 3.3 Increase of the Method's Rate of Convergence | p. 52 |
| 3.4 Method by Belotserkovskii and Yanitskii | p. 54 |
| 4 Modeling of the Flow of Continuous Media | p. 58 |
| 4.1 Procedure of the Monte Carlo Methods for Modeling the Flows of Rarefied Gas and Continuous Medium | p. 58 |
| 4.2 Method "Relaxation-Transfer" for a Solution of the Problems of Gas Dynamics in the Wide Range of the Degree of Rarefaction of a Medium (see Kogan et al. 83 ) | p. 62 |
| 4.3 Modeling of the Flows of Nonviscous Perfect Gas | p. 66 |
| 5 Solution of the Navier-Stokes Equations (Petrov 133-139 ) | p. 72 |
| 5.1 Formulation of the Problem, Initial and Boundary Conditions for the Navier-Stokes Equations in the Form by Helmholtz | p. 72 |
| 5.2 The General Properties of the Vertical Flow Arising by the Instantaneous Start of a Body from the State of Rest | p. 74 |
| 5.3 Initial Conditions for the Problem of the Instantaneous Start of a Body in a Viscous Fluid | p. 78 |
| 5.4 The General Algorithm of the Numerical Solution of an Initial-Boundary Problem for the Navier-Stokes Equations in the form by Helmholtz | p. 80 |
| 5.5 Solution of the Cauchy Problem for the Fokker-Plank Equation at Small Interval of Time | p. 88 |
| 5.6 The Numerical Solution of the Fokker-Plank Equation by the Method of Direct Statistical Modeling | p. 95 |
| 6 Studies of the Weakly Perturbed Flows of Rarefied Gas | p. 103 |
| 6.1 Determination of the Velocity of Slip | p. 103 |
| 6.2 Solution of the Problem of the Feeble Evaporation (Condensation) from the Plane Surface (see Korovkin, Khlopko 104 ) | p. 106 |
| 6.3 The Slow Motion of a Sphere in Rarefied Gas (Brownian Motion) | p. 108 |
| 6.4 The Coefficient of Diffusion and the Mean Shifting of a Brownian Particle in the Rarefied Gas (see Khlopkov 106 ) | p. 110 |
| 7 Study of the Flows About Different Bodies in Transitional Regime | p. 114 |
| 7.1 Flows About the Planar Bodies | p. 115 |
| 7.2 Flows About Axisymmetrical Bodies | p. 119 |
| 7.3 Influence of the Evaporation (Condensation) on the Aerodynamical Resistance of a Sphere by the Supersonic Flow About It | p. 125 |
| 7.4 Computation of the Steady Regime of a Flow About a Body and of the Profile Resistance in a Viscous Gas (See A.S. Petrov) | p. 128 |
| 8 Determination of the Aerodynamical Characteristics of the Returnable Space Systems (RSS) | p. 138 |
| 8.1 Methodics of the Description of a Surface | p. 138 |
| 8.2 Methodics of Calculation of the Aerodynamical Characteristics of the Flying Apparatus in the Conditions of a Free-Molecular Flow | p. 142 |
| 8.3 The Engineering Methodics of the Computation of Aerodynamical Characteristics of the Bodies of Complicated Form in a Transitional Regime (see Galkin, Eropheev, Tolstykh 85 ) | p. 143 |
| 8.4 The Results of the Flow About a Hypersonic Flying Apparatus "Clipper" (see Voronich, Zey Yar 225 ) | p. 145 |
| 9 The Flow About Blunted Bodies with the Addition of Heat (see Vorovich, Moiseev) | p. 165 |
| 9.1 The Main Features of a Method | p. 165 |
| 9.2 Description of the Algorithm | p. 167 |
| 9.3 The Approximational Properties | p. 170 |
| 9.4 The Algorithm and the Nets | p. 172 |
| 9.5 Direct Statistical Modeling of the Inviscid Flows About Blunted Bodies by the Presence of Energy Addition | p. 175 |
| 10 The General Models of Description of the Turbulent Flows | p. 187 |
| 10.1 Theoretical Methods of the Description of Turbulence | p. 187 |
| 10.2 Coherent Structures in the Turbulent Boundary Layer (see Khlopkov, Zharov, Gorelov 205 ) | p. 194 |
| 10.3 The Description of Turbulence with the Help of a Model of the Three-Wave Resonance | p. 204 |
| 10.4 The Fluidical Model of the Description of Turbulence (Belotserkovskii, Yanitskii) | p. 208 |
| 11 Studies of the Turbulent Flow of Fluid and Gas | p. 211 |
| 11.1 Modeling of a Turbulent Transition within the Boundary Layer Using Monte Carlo Method (see Zharov, Tun Tun, Khlopkov 223 ) | p. 211 |
| 11.2 Study of the Dissipation of Turbulent Spots (see Belotserkovskii, Yanitskii, Bukin 12,221 ) | p. 218 |
| 11.3 Evolution of the Vertical System in the Rarefied Gas (see Rovenskaya, Voronich, Zharov 222 ) | p. 219 |
| 12 The Possible Directions of Development of the Methods of Statistical Study | p. 228 |
| 12.1 Development of the Methods of Solution of Linear Problems | p. 228 |
| 12.2 Use of the Possibilities of the Model Equations | p. 232 |
| 12.3 Modeling of the Flows of Continuous Medium | p. 235 |
| 12.4 Modeling of the Turbulent Flows of Fluid and Gas | p. 240 |
| 12.5 Parallelization of the Statistical Algorithms (Bukin, Voronich, Shtarkin) | p. 245 |
| Conclusions | p. 253 |
| References | p. 257 |
