Meso

Question 1

What are the four particle methods in Mesoscopic scale?

Answer 1

Lattice Gas Automata
Lattice Boltzmann 1 & 2
Brownian Dynamics
Dissipative Particle Dynamics

Question 2

What is the physical range of particle methods in Mesoscopic range?

Answer 2

groups of atoms

Question 3

What does the Kinetic theory describe? (KT)

Answer 3

The evolution of a system’s state

Question 4

What is the goal of Kinetic theory? (KT)

Answer 4

to provide laws of macroscopic phenomena based on hypothesis of microscopic laws

Question 5

What are the premises of Kinetic theory? (KT)

Answer 5

1) system composed of many particles
2) microscopic dynamics laws are known(inter particle forces)
3) the governing macroscopic law is deducible from the micro-dynamics

Question 6

What is the goal of Liouville’s theorem? (KT)

Answer 6

to find an evolution equation for density

Question 7

What does the BBGKY hierarchy provide?(KT)

Answer 7

A systematic way to describe reduced distribution functions by relating N-particle dynamics to lower-order distribution

Question 8

What is the problem with the Bolztmann kinetic equation?

Answer 8

it is only true for suitable diluted gas condition

Question 9

What is the goal of Lattice Gas Automata? (LGA)

Answer 9

To reproduce the same fluid interactions as in Navier-Stokes, Boltzmann eq, etc.

Question 10

What are the limitations of Lattice Gas Automata? (LGA)

Answer 10

Galilean invariance is not valid
unphysical velocity-dependence in the equation of state
high level of numerical noise
valid only on low Mach number

Question 11

What are the basic features of Lattice Gas Automata model?(LGA)

Answer 11

1) Population of identical particles with the same speed
2) A totally discrete phase space
3) A minimum set of collision rules
4) An exclusion principle i.e. limits the number of particles per site

Question 12

What are the two-step dynamics in Lattice Gas Automata? (LGA)

Answer 12

free particle propagation
collision

Question 13

What are the differences between HPP and FHP model? (LGA)

Answer 13

HPP uses square lattice while FHP uses hexagonal lattice

HPP has at maximum four particles per site, while FHP has six

Question 14

In Lattice Gas Automata micro-dynamics, what properties must be satisfied? (LGA)

Answer 14

Mass and Momentum conservation

Question 15

In Lattice Gas Automata, what are the properties of the conservation equations?(LGA)

Answer 15

The structure of the momentum stress tensor depends on the geometry of the lattice

in HPP model, Euler equations are not recovered

isotropy is uniquely determined by the lattice geometry

Question 16

What are the advantages of Lattice Gas Automata? (LGA)

Answer 16

Efficient
Inherently Parallel
Unconditionally stable
Easy implementation of bounary condition
Mass and momentum exactly conserved

Question 17

What is the main problem with Lattice Gas Automata? (LGA)

Answer 17

It is intrinsically noisy

Question 18

How is the Lattice Boltzmann Method algorithm structured? (LBM2)

Answer 18

1) Initialisation
2) caculate the microscopic quantities
3) calculate the equilibrium distribution
4) collision through BGK operator
5) application of the boundary condition
6) repeat to 2)

Question 19

What are the Boundary Conditions in LBM2? (LBM2)

Answer 19

on wall : bounce-back condition
periodic

Question 20

What is the main idea of Lattice Boltzmann Method? (LBM1 & LBM2)

Answer 20

to translate the Lattice Gas Automata into a related Boltzmann model

Question 21

What are the issues of Lattice Boltzmann 2?(LBM2)

Answer 21

lost of connection to micro-physics
no guarantee of stability
numerical instability for a high reynolds number

Question 22

What are some phenomenons that occur at mesoscale?

Answer 22

fluid mixtures
emulsions
colloidal suspensiions
aggregation
phase separation

Question 23

Which three forces are included in the Dissipative Particle Dynamics? (DPD)

Answer 23

Conservative
Dissipative
Stochastic

Question 24

What is the Fluctuation Dissipation Theorem? (DPD)

Answer 24

a tool in statistical physics for predicting the behaviour of non-equilibrium thermodynamical systems

Question 25

How is the Dissipative Particle Dynamics algorithm formulated?

Answer 25

similar to Molecular Dynamics

Question 26

What's the main difference between the HPP model and the FHP model ?

Answer 26

HPP is not isotropic (wrong behaviour of the fluid) whereas the isotropy of FHP is fully determined.

Question 27

Of what the collision operator is composed in the Boltzmann equation ?

Answer 27

Incoming and outcoming distribution

Question 28

What are the main differences between LGA and LBM 1 ?

Answer 28

-The binary variables (LGA) are replaced by continuous distribution functions (LBM 1) -LBM 1 less noisy than LGA

Question 29

What is the common point between LGA and LBM 1 but different to LBM 2

Answer 29

The none Galilean invariance and the velocity-dependency of the state equation

Question 30

What is the BGK operator ?

Answer 30

It's an approximation of the collision operator used to reduce the complexity (from multiple scale relaxation process to one single parameter)

Question 31

For which Ma the LBM 1 is applicable ?

Answer 31

For low Ma due to a low velocity approximation in the coarse-grained dynamics reduction

Question 32

Which technic we use to go from the LGA to LBM 1 ? And why ?

Answer 32

The coarse-grained dynamics to reduce the complexity of the system.

Question 33

What are the steps of the coarse-grained dynamics ?

Answer 33

1) Probabilistic description 2) Linking microscopic to macroscopic dynamics (mass and momentum conservation properties) 3) Reconstruction with Fermi-Dirac equilibrium distribution (binary to continuous) 4) Reconstruction from low-speed approximation 5) Conservation equation (according to the lattice)

Question 34

Why the DPD method needs of a Fluctuation-Dissipation Theorem (FDT) ?

Answer 34

It ensures an equilibrium between random and dissipative forces.