Discreet Element Method

Question 1

Describe discrete element method?

Answer 1

● DEM is a simulation technique applicable to large-sized particles

● Combination of Newton’s law of motion, Computational Power and Process Knowledge

Question 2

Briefly describe the basic algorithm of DEM

Answer 2

① State the initial conditions (position, velocity or number of states)
② Detect Collision (must be yes)
③ Calculate Forces (governed by Newton’s LoM)
④ Change and update the state (acceleration)

Question 3

How to choose the time step?

Answer 3

Small enough to resolve the fastest collision event

Question 4

How to check for collision for spherical particles?

Answer 4

Generally has two ways:
① Brute Force (slow)
- 1 object at a time
- O(N²) check ~ if N = 10¹⁰, need 10²⁰ check

② Neighboring Cells (fast)

• get rid of particles that are very far away from the particle of interest
• system is divided into cells

Question 5

Give two different simulation scheme

Answer 5

Time-driven and Event-driven

① Time-driven

• choose Δt that can resolve the fastest collision
• trial and error?
• there is a possibility of overlap since we only know ti and tf

② Event-driven

• progress time step after each (single) collision
• similar to verlet algorithm (?) (MD)
• allows for easier/more efficient collision detection
• not applicable for non-dilute system since Δt will be very low and system will crash
• difficult to take into account other forces

Question 6

Write the equation that states the general criteria for collision in spheres

Answer 6

dij < ri + rj

where dij is the distance between radius ri and rj

Question 7

Enumerate some models for NON-spherical particles

Answer 7

① Multi-sphere Approximation
- several spheres to mimic the shape

② Polyhedra Approximation
- Polyhedron described by corners and faces based on centre of gravity

③ Superquadrics
- there is an analytical function for this with the parameter of sphere shape and coordinates

Question 8

Briefly explain how to detect collision for NON-spherical particles

Answer 8

① Multi-sphere model
- boundary method

② Polyhedra
- common plane

③ Superquadrics
- analytical function

Question 9

A system can be fluid and particle or both, what is the idea behind this?

Answer 9

● Fluids + Particles
Governed by Euler - Lagrange
Navier Stokes
Newton’s LoM

● Multi-phase
if the system is supersaturated
Governed by Euler - Euler (continuous)
Navier Stokes

Question 10

Express in an equation the condition for collision in CP

Answer 10

Common plane of objects A and B:
● Centroids of A and B are located on opposite sides
(A negative side, B positive side).
● The gap dB-dA is a maximum.
● dB = -dA

There is contact when dA > 0 and dB < 0, gap is negative

Question 11

Enumerate different forces

Answer 11

● Gravity
● Friction
● Adhesion
● Drag Force
● Electrostatic

Question 12

What is the two governing ideas for collision or contact?

Answer 12

① Elastic Collision F = -k Δx

② Plastic Collision F = -b Δv

where k and b are both material property