Lattice Gas AutomataIntroduction to Computational Science

University of Amsterdam

Amir Masoud Abdol

Lattice Boltzmann Model

▪ Computational Fluid Dynamics

▪ Simulate the flow of a Newtonian Fluid with collision models.

▪ Instead of solving Navier-Stokes Equations

Lattice Gas Automata

Its a Cellular Automata method to simulate fluid dynamics by considering according to Lattice Boltzmann Model.

▪ Particles can move in only one directions.

▪ There cannot exist more than one particle at each node heading in the same direction.

▪ The magnitude of the particle velocity is fixed.

▪ A particle cannot remain stationary.

▪ Advantages:

▪ Can be implemented in complex boundaries

▪ No numerical error

▪ Easy to parallelize

▪ Less computation

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HPP: Model

It introduced in 1973 by Hardy, Pomeau and de Pazzis

It is deterministic

It supports 4 different velocities

Particles cannot move diagonally

vortices produced by the HPP model are square-shaped.

Simple to implement

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HPP: Collisions and Propagations

Collisions:

Two possible collisions

Propagation:

Follow their path

Boundaries:

No boundaries

Periodic boundaries

Closed boundaries with reflective behaviors

HPP: Implementation

Velocities Bits Integer

C1 00001 1

C2 00010 2

C3 00100 4

C4 01000 8

Solid 10000 16

Using Square Lattice (2D Array)

Need 5 bits to implement the lattice

Simple Collision Table

Bitwise operations

Presence of particle can be decided by binary operations

preCollision

postCollision

Integer

Binary

C1+C3 C2+C4 5<>10 00101<>01010

C2+C4 C1+C3 10<>5 01010<>00101

int velocityInC2(int totalVelocity){ return (totalVelocity >> 1) & 1;}

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FHP: Model

It introduced in 1986 by Uriel Frisch, Brosl Hasslacher and Yves Pomeau

It is not deterministic

It supports 6 different velocities

Particle can move diagonally

More Realistic

Difficult to Implement

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FHP: Collisions and Propagations

Collisions

Two way collisions

Three way collisions

Random bit decide about the possible post-collision

Propagations

Just simply moving in their direction

Bounce Back

Reflection

FHP: Implementation

Velocities

Binary Integer

C1 00000001

1

C2 00000010

2

C3 00000100

4

C4 00001000

8

C5 00010000

16

C6 00100000

32

SOLID 01000000

64

RANDOM 10000000

128

Implementing Hexagonal Lattice with 2D array

Using Collisions Table

Contain all possible collisions

Boundaries:

Closed

Bounce Back Rules

No Boundaries

Periodic Boundaries

preCollision

postCollision

Integer

C1+C4 C2+C5C3+C6

9 <> 189 <> 36

C1+C3+C5 C2+C4+C6 21 <> 42

For instance:10010010 C2+C5+RANDOM

Thanks!Any questions?