| Preface |
|
v | |
|
|
|
1 | (22) |
|
1 The Main Equations and Approaches to Solutions of the Problems in Rarefied Gas Dynamics |
|
|
23 | (7) |
|
1.1 The Main Equations in Rarefield Gas Dynamics |
|
|
23 | (2) |
|
1.2 The Main Approaches to the Construction of Statistical Algorithms |
|
|
25 | (1) |
|
1.3 Connection of the Stationary Modeling with the Solution of Equation |
|
|
26 | (2) |
|
1.4 Construction of the Method of Direct Statistical Modeling |
|
|
28 | (2) |
|
2 Development of the Numerical Methods of Solution of the Linear Kinetic Equations |
|
|
30 | (13) |
|
2.1 The Perfection of VGK Method (Vlasov, Gorelov, Kogan) |
|
|
30 | (5) |
|
2.2 Modification of the Vlasov's Method for the Solution of Linear Problems |
|
|
35 | (3) |
|
2.3 Method of Solution of the Linearized Boltzmann's Equation |
|
|
38 | (5) |
|
3 Methods of Solution of the Nonlinear Problems in Rarefied Gas Dynamics |
|
|
43 | (15) |
|
3.1 Method of Solution of the Model Equation Based on a Stationary Modeling |
|
|
43 | (3) |
|
3.2 The Possibilities of the Scheme of Splitting for the Solution of Kinetic Equations |
|
|
46 | (6) |
|
3.3 Increase of the Method's Rate of Convergence |
|
|
52 | (2) |
|
3.4 Method by Belotserkovskii and Yanitskii |
|
|
54 | (4) |
|
4 Modeling of the Flow of Continuous Media |
|
|
58 | (14) |
|
4.1 Procedure of the Monte Carlo Methods for Modeling the Flows of Rarefied Gas and Continuous Medium |
|
|
58 | (4) |
|
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) |
|
|
62 | (4) |
|
4.3 Modeling of the Flows of Nonviscous Perfect Gas |
|
|
66 | (6) |
|
5 Solution of the Navier-Stokes Equations (Petrov133-139) |
|
|
72 | (31) |
|
5.1 Formulation of the Problem, Initial and Boundary Conditions for the Navier-Stokes Equations in the Form by Helmholtz |
|
|
72 | (2) |
|
5.2 The General Properties of the Vertical Flow Arising by the Instantaneous Start of a Body from the State of Rest |
|
|
74 | (4) |
|
5.3 Initial Conditions for the Problem of the Instantaneous Start of a Body in a Viscous Fluid |
|
|
78 | (2) |
|
5.4 The General Algorithm of the Numerical Solution of an Initial-Boundary Problem for the Navier-Stokes Equations in the form by Helmholtz |
|
|
80 | (8) |
|
5.5 Solution of the Cauchy Problem for the Fokker-Plank Equation at Small Interval of Time |
|
|
88 | (7) |
|
5.6 The Numerical Solution of the Fokker-Plank Equation by the Method of Direct Statistical Modeling |
|
|
95 | (8) |
|
6 Studies of the Weakly Perturbed Flows of Rarefied Gas |
|
|
103 | (11) |
|
6.1 Determination of the Velocity of Slip |
|
|
103 | (3) |
|
6.2 Solution of the Problem of the Feeble Evaporation (Condensation) from the Plane Surface (see Korovkin, Khlopkov104) |
|
|
106 | (2) |
|
6.3 The Slow Motion of a Sphere in Rarefied Gas (Brownian Motion) |
|
|
108 | (2) |
|
6.4 The Coefficient of Diffusion and the Mean Shifting of a Brownian Particle in the Rarefied Gas (see Khlopkov106) |
|
|
110 | (4) |
|
7 Study of the Flows About Different Bodies in Transitional Regime |
|
|
114 | (24) |
|
7.1 Flows About the Planar Bodies |
|
|
115 | (4) |
|
7.2 Flows About Axisymmetrical Bodies |
|
|
119 | (6) |
|
7.3 Influence of the Evaporation (Condensation) on the Aerodynamical Resistance of a Sphere by the Supersonic Flow About It |
|
|
125 | (3) |
|
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) |
|
|
128 | (10) |
|
8 Determination of the Aerodynamical Characteristics of the Returnable Space Systems (RSS) |
|
|
138 | (27) |
|
8.1 Methodics of the Description of a Surface |
|
|
138 | (4) |
|
8.2 Methodics of Calculation of the Aerodynamical Characteristics of the Flying Apparatus in the Conditions of a Free-Molecular Flow |
|
|
142 | (1) |
|
8.3 The Engineering Methodics of the Computation of Aerodynamical Characteristics of the Bodies of Complicated Form in a Transitional Regime (see Galkin, Eropheev, Tolstykh85) |
|
|
143 | (2) |
|
8.4 The Results of the Flow About a Hypersonic Flying Apparatus "Clipper" (see Voronich, Zey Yar225) |
|
|
145 | (20) |
|
9 The Flow About Blunted Bodies with the Addition of Heat (see Vorovich, Moiseev) |
|
|
165 | (22) |
|
9.1 The Main Features of a Method |
|
|
165 | (2) |
|
9.2 Description of the Algorithm |
|
|
167 | (3) |
|
9.3 The Approximational Properties |
|
|
170 | (2) |
|
9.4 The Algorithm and the Nets |
|
|
172 | (3) |
|
9.5 Direct Statistical Modeling of the Inviscid Flows About Blunted Bodies by the Presence of Energy Addition |
|
|
175 | (12) |
|
10 The General Models of Description of the Turbulent Flows |
|
|
187 | (24) |
|
10.1 Theoretical Methods of the Description of Turbulence |
|
|
187 | (7) |
|
10.2 Coherent Structures in the Turbulent Boundary Layer (see Khlopkov, Zharov, Gorelov205) |
|
|
194 | (10) |
|
10.3 The Description of Turbulence with the Help of a Model of the Three-Wave Resonance |
|
|
204 | (4) |
|
10.4 The Fluidical Model of the Description of Turbulence (Belotserkovskii, Yanitskii) |
|
|
208 | (3) |
|
11 Studies of the Turbulent Flow of Fluid and Gas |
|
|
211 | (17) |
|
11.1 Modeling of a Turbulent Transition within the Boundary Layer Using Monte Carlo Method (see Zharov, Tun Tun, Khlopkov223) |
|
|
211 | (7) |
|
11.2 Study of the Dissipation of Turbulent Spots (see Belotserkovskii, Yanitskii, Bukin 12,221) |
|
|
218 | (1) |
|
11.3 Evolution of the Vertical System in the Rarefied Gas (see Rovenskaya, Voronich, Zharov 222) |
|
|
219 | (9) |
|
12 The Possible Directions of Development of the Methods of Statistical Study |
|
|
228 | (25) |
|
12.1 Development of the Methods of Solution of Linear Problems |
|
|
228 | (4) |
|
12.2 Use of the Possibilities of the Model Equations |
|
|
232 | (3) |
|
12.3 Modeling of the Flows of Continuous Medium |
|
|
235 | (5) |
|
12.4 Modeling of the Turbulent Flows of Fluid and Gas |
|
|
240 | (5) |
|
12.5 Parallelization of the Statistical Algorithms (Bukin, Voronich, Shtarkin) |
|
|
245 | (8) |
| Conclusions |
|
253 | (4) |
| References |
|
257 | |
Rohkem infot World Scientific e-raamatute kohta