Елизарова Татьяна Геннадьевна

Elizarova Tatiana Gennadievna

Contents of book

Introduction

1 Construction of gasdynamic equations

1. Averaging procedure
2. Integral form of conservative laws
3. Differential form of conservative laws
4. Euler and Navier—Stokes equations
5. Quasi-gasdynamic and quasi-hydrodynamic equations

2 Elements of kinetic theory

1. Boltzmann equation
2. Equilibrium distribution function and Euler equations
3. Navier-Stokes system of equations
4. Bhatnagar-Gross-Krook equation
5. Averaged values for particle motion
6. Coefficients in transport phenomena
7. Numerical simulation of rarefied flows
8. Kinetic-consistent numerical algorithm

3  Quasi-gasdynamic equations

1. Model kinetic equation
2. Kinetic equation and construction of the QGD system
3. QGD system in form of conservation laws
4. Dissipative coefficients
5. Navier-Stokes system as an asymptotic of QGD system
6. QGD system for flows with external heat sources
7. Entropy balance equation

4  QGD equations and coordinate systems

1. QGD equations in arbitrary coordinate system
2. Cartesian coordinate system
3. Cylindrical coordinate system

5 Numerical algorithms for gas dynamic flows

1. Equation system for flat two-dimensional flows
2. Equation system for cylindrical two-dimensional flows
3. Boundary conditions
4. Normalized form of equations
5. Finite-difference approximation
6. Artificial dissipation
7. Strong discontinuity step evolution problem
8. Flow around a cylindrical obstacle
9. Flow in a channel with a forward step
10. Numerical simulation of subsonic flows
11. Stability and accuracy of QGD algorithms

6 Numerical algorithms for unstructured grids

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

7  Numerical algorithms for incompressible flow

1. Quasi-hydrodynamic system of equations
2. Numerical algorithm
3. Backward-faced step flow in a channel
4. Thermal convection in a square cavity
5. Thermal convection for low Prandtl numbers
6. Marangony convection in microgravity
7. Flow in a cubic cavity with a moving wall

8. QGD equations for non-equilibrium flows

1. Molecular model and distribution functions
2. Coordinate systems and certain integrals
3. Construction of moment equations
4. Calculation of exchanging terms
5. QGDR equations
6. Examples of numerical computations

9 QGD equations for a binary gas mixture

1. Basic kinetic model
2. Construction of moment equations
3. Calculation of exchanging terms
4. Determination of collision frequencies
5. QGD equations for a gas mixture
6. One-fluid approximation
7. QGD system for a flat one-dimensional flow
8. Shock-wave structure in Helium-Xenon mixture
9. 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