Solutions to benchmark 4 poster presented at CHiMaD annual meeting 2019

1. This work was performed under the following financial assistance award 70NANB19H005 from U.S. Department of Commerce, National Institute of Standards
and Technology as part of the Center for Hierarchical Materials Design (CHiMaD). chimad.northwestern.edu
Benchmark III Problems: Fluid Flow & Electrochemistry
Fluid Flow
• Stokes Flow: Incompressible fluid & low Reynolds number
u is the local fluid velocity field, 𝛍 the dynamic viscosity, p
the local pressure, g field of external acceleration, and 𝛒0
the fluid density
Pressure and velocity components for 2D flow
Electrochemical Problem
• Simplified electrochemistry: Charge conservation,
distribution, and mass diffusion
Initial (left) and final (right) concentration field under the
evolution of diffusion with an applied external potential
Continuity
Momentum
P
Vy
Vx
Reveal L2 error
resulting from
meshing and/or
solver
Mass Diffusion
Electrochemical Potential
Charge Distribution
Without external
potential, mass
pattern is different
Future Plans
 Benchmark problems on homogeneous and heterogeneous nucleation
 Uploading to PFHub website https://pages.nist.gov/pfhub/
OBJECTIVES AND GOALS
 The Phase Field Method is a common mesoscale modeling
technique
 Many phase field codes exist using many numerical
methods and approaches
 We need confidence to use quantitative phase field results
in Integrated Computational Materials Engineering
Phase Field Methods
Community-Driven Benchmark Problems for Phase Field Modeling
A.M. Jokisaari1, W. Wu2, P.W. Voorhees3, J.E. Guyer4, J. Warren4, D. Hweeler4, O.G. Heinonen2,5
1Idaho National Laboratory, 2Argonne National Laboratory, 3Northwestern University, 4National Institute of Standards and Technology, 5Northwestern-
Argonne Institute of Science and Technology
 Standard benchmark problems allow comparison and testing
• Models, algorithms, implementations
• Solution accuracy, solver optimizations, code
modifications
 Benchmark problems are also pedagogical tools for teaching
phase field methods
 Website for benchmark problems: https://pages.nist.gov/pfhub/