# Contents of the English book

Introduction

1 Construction of gasdynamic equations

2 Elements of kinetic theory

3 Quasi-gasdynamic equations

4 QGD equations and coordinate systems

5 Numerical algorithms for gas dynamic flows

- Averaging procedure
- Integral form of conservative laws
- Differential form of conservative laws
- Euler and Navier—Stokes equations
- Quasi-gasdynamic and quasi-hydrodynamic equations

2 Elements of kinetic theory

- Boltzmann equation
- Equilibrium distribution function and Euler equations
- Navier-Stokes system of equations
- Bhatnagar-Gross-Krook equation
- Averaged values for particle motion
- Coefficients in transport phenomena
- Numerical simulation of rarefied flows
- Kinetic-consistent numerical algorithm

3 Quasi-gasdynamic equations

- Model kinetic equation
- Kinetic equation and construction of the QGD system
- QGD system in form of conservation laws
- Dissipative coefficients
- Navier-Stokes system as an asymptotic of QGD system
- QGD system for flows with external heat sources
- Entropy balance equation

4 QGD equations and coordinate systems

- QGD equations in arbitrary coordinate system
- Cartesian coordinate system
- Cylindrical coordinate system

5 Numerical algorithms for gas dynamic flows

- Equation system for flat two-dimensional flows
- Equation system for cylindrical two-dimensional flows
- Boundary conditions
- Normalized form of equations
- Finite-difference approximation
- Artificial dissipation
- Strong discontinuity step evolution problem
- Flow around a cylindrical obstacle
- Flow in a channel with a forward step
- Numerical simulation of subsonic flows
- Stability and accuracy of QGD algorithms

6 Numerical algorithms for unstructured grids

- Grid selection and definition of finite volume
- Approximation of the system in whole
- Approximation of partial derivatives
- Numerical algorithms for two-dimensional flows
- Approximation of boundary conditions
- Computation of the flow around a cylinder

7 Numerical algorithms for incompressible flow

- Quasi-hydrodynamic system of equations
- Numerical algorithm
- Backward-faced step flow in a channel
- Thermal convection in a square cavity
- Thermal convection for low Prandtl numbers
- Marangony convection in microgravity
- Flow in a cubic cavity with a moving wall

8. QGD equations for non-equilibrium flows

- Molecular model and distribution functions
- Coordinate systems and certain integrals
- Construction of moment equations
- Calculation of exchanging terms
- QGDR equations
- Examples of numerical computations

9 QGD equations for a binary gas mixture

- Basic kinetic model
- Construction of moment equations
- Calculation of exchanging terms
- Determination of collision frequencies
- QGD equations for a gas mixture
- One-fluid approximation
- QGD system for a flat one-dimensional flow
- Shock-wave structure in Helium-Xenon mixture
- Problem of Argon-Helium diffusion

Appendices

A Example of construction of the QGD system

B Gas flow in microchannels

C Shock-wave structure

D Backward- faced step flow in a channel. Laminar-turbulent transition.

Citations