Simulating interface evolution using a parallel space-time approach: Space-time adaptivity for the phase field equations

Kumar Saurabh, Biswajit Khara and Baskar Ganapathysubramanian (Iowa State University)
Milinda Fernando, Masado Ishii and Hari Sundar\textsuperscript (University of Utah)

Interface evolution (solidification, melting, phase-separation) phenomena exhibit spatially and temporally localized regions of steep gradients. Conventional approaches (i.e. time marching approaches) utilize localized adaptivity in space, but generally utilize global adaptivity in time. Here, we consider time as an additional dimension and simultaneously solve for the unknown in large blocks of time (i.e. in space-time). We focus on space-time solutions of a generalized class of equations called the phase-field equations. We formulate a variational multiscale (VMS) based space-time strategy that allows us to (a) exploit parallelism not only in space but also in time, (b) gain high order accuracy in time, and (c) exploit adaptive refinement approaches to locally refine the region of interest in both space and time. We illustrate this approach with several canonical problems including melting and solidification of complex dendritic/snowflake structures and phase separation simulation.