The document summarizes the results of simulations run by Jason Luce and Beck Andrews of the University of Michigan at the CHiMaD Phase Field Methods Workshop III & Hackathon in May 2016. It includes summaries of simulations of crystal growth (Q1) reporting on symmetry, velocity, system size effects, and workflow. It also includes simulations coupling phase field models with mechanics (Q2) showing 3D representations of results, a plot of energy over time, and measurements of aspect ratios indicating the mechanics solver is working but the concentration field is slow to change from initial conditions. Details on computational resources used are also provided.

1. PRISMS CENTER (TEAM 4)
Jason Luce and Beck Andrews
University of Michigan
CHiMaD Phase Field Methods Workshop III & Hackathon
MAY 3-5, 2016

2. Question 1

3. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Movie of Evolution

4. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Movie of Evolution

5. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Movie of Evolution
Six-fold symmetry appears to work
𝜃0 implementation (not shown) gave smaller offset
than expected [bug]

6. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Tip Velocity vs Time
• Assumptions- tip velocity is highest velocity in system
• v1: velocity based on energy conservation
– No gradient in particle
• v2: velocity of signed distance function
– In interface, max 𝛻𝜙 = 1/ 2
𝑣1 = max 𝐷 𝑛 ⋅ 𝛻𝑢 ≈ max 𝐷
𝛻𝜙
( 𝛻𝜙 + 𝜖)
⋅ 𝛻𝑢
𝑣2 = max
𝜕𝜙
𝜕𝑡
1
𝛻𝜙
≈ max
𝜕𝜙
𝜕𝑡
2

7. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Tip Velocity vs Time
Small system, 20x20 Large system, 100x100

8. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Workflow (flowchart)
Copy existing application folder
(coupledCahnHilliardAllenCahn,
coupledCahnHilliardMechanics)
Modify model file
(coupledCHMechanics.h,
coupledCHAC.h)
Modify residual expressions
(parameters.h)
Modify BCs, ICs (main.cc)
Modify simulation parameters
(parameters.h)
SIMULATE!!!Analyze .vtu output in VisIt

9. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q1 – Details
• DOF: 198147, 4922883
• Δ𝑥~0.16, Δ𝑡 = 10−4
• # cores: 16
• Core hours (100k increments): 1.3, 18
• Wall clock time: 4.7 min, 1.1 hrs
• Per-increment time (ms): 2.1, 40
• https://github.com/prisms-center/phaseField
– parameters.h, main.cc, and model files modified per
uploaded code

10. Question 2

11. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q2 – 3D representation of result
2a)

12. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q2 – 3D representation of result
2b)

13. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q2 – 3D representation of result
2c)

14. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q2 – Energy vs “Time” (Plot)
2a)
Energy
Time

15. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q2 – Measurement of Aspect Ratio along
principal directions
• Measurements of Aspect Ratio were performed using
Visit visualization software
– 2a) 1 along all directions, as expected
– 2b) Mechanics solver appears to be working as expected, but
concentration field does not change accordingly (ratio still very
close to 1 for all axis
– 2c) Similar to 2b, the mechanics solver appears to be working
as expected, but the concentration field is again slow to
change – axis ratio essentially unchanged from initial conditions

16. CHiMaD Phase Field Methods Workshop III & Hackathon – MAY 3-5, 2016
Q2 – Details
• # cores: 4 cores (Laptop)
• Wall clock time: 10-20 min
• Core hours: 40-80 min
• PRISMS code can be found at:
https://github.com/prisms-center