Benchmark problems for numerical implementations of phase field models

Abstract

We present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative.

Phase field benchmark problems for dendritic growth and linear elasticity

“…MOOSE-based simulations are performed for both problems, while the bespoke code is used only for the first problem on solidification and dendritic growth. We have also used MOOSE to provide example solutions for the first set of benchmark problems [22].…”

“…However, we follow the benchmark problem design principles given in Ref. [22] to create (or select from the literature) a problem that captures the essential physics of the given phenomenon, yet is simplified and easy to implement. This is particularly important for the dendritic growth problem, as simulated microstructures can be extremely sensitive to numerical and model parameterization choices [19,24].…”

“…We choose problem formulations and benchmark metrics that balance the need for nontrivial solutions with computational resource requirements and the investment of human effort, and we intend that these problems are used by the community to understand how numerical methods impact results by comparing different results (see Ref. [22] for a detailed discussion). Importantly, the benchmark problem effort includes significant community involvement regarding problem proposal, design and vetting.…”

“…In particular, we address models that include coupled physics, as these can pose significant numerical challenges. The first set of problems focus on the diffusion of solute and the growth of a second phase [22], while this set involves solidification and dendritic growth as well as linear elasticity. To support community involvement, we have developed a website (https://pages.nist.gov/pfhub/), which serves as a repository for the problem statements and the results from different numerical implementations.…”

New Methods for Understanding and Controlling the Self-Assembly of Reacting Systems Using Coarse-Grained Molecular Dynamics

“…The authors attributed this discrepancy to the fact that the reaction becomes diffusion controlled at later stages of curing which was not explicitly taken into account by the constitutive model. Another continuum-scale empirical model called the phase field modeling method 45 has been shown to have practical applications for predicting phase separated morphologies.…”