  The evolution of interfaces is intrinsic to many physical processes ranging
from cavitation in fluids to recrystallization in solids. Computational
modeling of interface motion entails a number of challenges, many of which are
related to the range of topological transitions that can occur over the course
of the simulation. Microstructure evolution in a polycrystalline material that
involves grain boundary motion is a particularly complex example due to the
extreme variety, heterogeneity, and anisotropy of grain boundary properties.
Accurately modeling this process is essential to determining
processing-structure-property relationships in polycrystalline materials
though. Simulations of microstructure evolution in such materials often use
diffuse interface methods like the phase field method that are advantageous for
their versatility and ease of handling complex geometries but can be
prohibitively expensive due to the need for high interface resolution. Discrete
interface methods require fewer grid points and can consequently exhibit better
performance but have received comparatively little attention, perhaps due to
the difficulties of maintaining the mesh and consistently implementing
topological transitions on the grain boundary network. This work explicitly
compares a recently-developed discrete interface method to a multiphase field
method on several classical problems relating to microstructure evolution in
polcrystalline materials: a shrinking spherical grain, the steady-state triple
junction dihedral angle, and the steady-state quadruple point dihedral angle.
In each case, the discrete method is found to meet or outperform the multiphase
field method with respect to accuracy for comparable levels of refinement,
demonstrating its potential efficacy as a numerical approach for microstructure
evolution in polycrystalline materials.
