Phase Field Benchmark Problems Targeting Fluid Flow and Electrochemistry

Abstract

In this work, a third set of benchmark problems for phase field models are presented. These problems are being jointly developed by the Center for Hierarchical Materials Design (CHi- MaD) and the National Institute of Standards and Technology (NIST) along with input from the phase field community. The first problem in this third set targets Stokes flow, with a par- ticular emphasis on flow around an obstruction placed asymmetrically in the domain. While Stokes flow is not traditionally in the canon of phase field problems, it is a class of problems gaining importance in areas such as filtration and water purification. The second problem deals with coupled Cahn-Hilliard diffusion and electrostatic forces, which is an important area in energy storage and battery sciences. We present our own solutions, discuss sources of numerical errors for the Stokes problem, and simple checks to avoid fundamental issues in the coupled diffusion-electrostatics problem. The latter problem contains some subtleties that we expand on in an Appendix.