Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows [E-Book] / by V. V. Aristov
This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russ...
Saved in:
Full text |
|
Personal Name(s): | Aristov, V. V., author |
Imprint: |
Dordrecht :
Springer,
2001
|
Physical Description: |
XVII, 302 p. online resource. |
Note: |
englisch |
ISBN: |
9789401008662 |
DOI: |
10.1007/978-94-010-0866-2 |
Series Title: |
/* Depending on the record driver, $field may either be an array with
"name" and "number" keys or a flat string containing only the series
name. We should account for both cases to maximize compatibility. */?>
Fluid Mechanics and its Applications ;
60 |
Subject (LOC): |
- 1 The Boltzmann Equation as a Physical and Mathematical Model
- 1.1 Different mathematical forms of the kinetic equation
- 1.2 Peculiarities of kinetic approach for describing physical properties
- 1.3 Formulation of problems and boundary conditions
- 1.4 The forms of the Boltzmann equations in some physical cases
- References
- 2 Survey of Mathematical Approaches to Solving the Boltzmann Equation
- 2.1 General notes on classification of methods
- 2.2 Methods combining analytical and numerical features. Some partial solutions
- 2.3 Approaches based on kinetic models
- 2.4 Numerical simulation methods
- 2.5 Direct simulation Monte Carlo methods
- 2.6 Methods of direct integration
- 2.7 Comparison of direct integration and direct simulation
- References
- 3 Main Features of the Direct Numerical Approaches
- 3.1 Discrete velocities and approximation in velocity space
- 3.2 Approximation in physical space. Finite-difference schemes and iterations
- 3.3 Splitting method
- 3.4 Finite volume scheme
- 3.5 Evaluation of the collision integrals by Monte Carlo technique
- 3.6 Quasi Monte Carlo technique
- References
- 4 Deterministic (Regular) Method for Solving the Boltzmann Equation
- 4.1 General features of the method
- 4.2 Approach to approximation of the collision integrals. Integration over velocity space
- 4.3 Exact evaluation of integrals over impact parameters
- 4.4 Approximation of the collision integrals by quadratic form with constant coefficients
- 4.5 Simplification for velocity space in the case of isotropic symmetry
- References
- 5 Construction of Conservative Scheme for the Kinetic Equation
- 5.1 Different definitions of conservativity
- 5.2 Conservative splitting method
- 5.3 Characteristics and advantages of the conservative schemes
- 5.4 Practical verification of the method
- 5.5 Conservative method for gas mixtures
- References
- 6 Parallel Algorithms for the Kinetic Equation
- 6.1 Parallel implementation for the direct methods
- 6.2 Several parallel algorithms
- 6.3 Examples of parallel applications of the algorithms
- References
- 7 Application of the Conservative Splitting Method for Investigating Near Continuum Gas Flows
- 7.1 Some approaches to solving the Boltzmann equation for weakly rarefied gas
- 7.2 Asymptotic kinetic schemes approximating the Euler and Navier-Stokes equations
- 7.3 Schemes for flows at low Knudsen numbers
- References
- 8 Study of Uniform Relaxation in Kinetic Gas Theory
- 8.1 Spatially uniform (homogeneous) relaxation problem
- 8.2 Obtaining the test solutions for isotropic relaxation
- 8.3 Some examples of the relaxation problem solutions
- 8.4 Uniform relaxation for gas mixtures
- References
- 9 Nonuniform Relaxation Problem as a Basic Model for Description of Open Systems
- 9.1 Formulation of the problem and solution methods
- 9.2 Nonclassical behavior of macroscopic parameters
- 9.3 Behavior of the distribution function and macroscopic parameters
- 9.4 Possible entropy decrease
- 9.5 Some generalizations
- References
- 10 One-Dimensional Kinetic Problems
- 10.1 The problem of heat transfer
- 10.2 Shock wave structure
- 10.3 Flow in the field of an external force
- 10.4 Recondensation of a mixture in a force field
- References
- 11 Multi-Dimensional Problems. Study of Free Jet Flows
- 11.1 Possibilities of direct integration approaches for studying multi-dimensional problems
- 11.2 Formulation of the problem and numerical scheme
- 11.3 Free plane jet
- 11.4 Axisymmetric and three-dimensional free jet flows
- References
- 12 The Boltzmann Equation and the Description of Unstable Flows
- 12.1 Main notions
- 12.2 Boltzmann and Navier-Stokes description
- 12.3 Mathematical apparatus
- 12.4 Some results of numerical modelling.
- References
- 13 Solutions of some Multi-Dimensional Problems
- 13.1 Unsteady problem of a shock wave reflection from a wedge
- 13.2 Solution for focusing of a shock wave
- 13.3 Study of flows in elements of cryovacuum devices
- 13.4 Flows in the vacuum cryomodulus
- 13.5 Two-component mixture flows with cryocondensation
- References
- 14 Special Hypersonic Flows and Flows with Very High Temperatures
- 14.1 Special hypersonic flows
- 14.2 Unsteady flows caused by a powerful point discharge of a finite gaseous mass
- 14.3 Asymptotic solution at t ? 0
- 14.4 Numerical analysis. Asymptotic solution at t ? ?
- 14.5 Scattering of impulsive molecular beam
- References.