A novel method for capturing two-dimensional, thin, under-resolved material configurations, known as “filaments" is presented in the context of interface reconstruction. This technique uses a partitioning procedure to detect disconnected regions of material in the advective preimage of a cell (indicative of a filament) and makes use of the existing functionality of the Multimaterial Moment-of-Fluid interface reconstruction method to accurately capture the under-resolved feature, while exactly conserving volume. An algorithm for Adaptive Mesh Refinement in the presence of laments is developed so that refinement is introduced only near the tips of laments and where the Moment-of-Fluid reconstruction error is still large. Comparison to the standard Moment-of-Fluid method is made. It is demonstrated that using filament capturing at a given resolution yields gains in accuracy comparable to introducing an additional level of mesh refinement at significantly lower cost. This is research with M. Jemison and M. Shashkov.

Mark Sussman was born in San Diego, California in 1966. He graduated from San Diego State University in 1986 (Bachelor's degree in Applied Mathematics, minor in physics and computer science), and University of California, Los Angeles in 1994 (PhD degree in mathematics, advisor S. Osher). Mark Sussman's employment history includes two years as a postdoc at Lawrence Livermore/Berkeley National Laboratory, three years as a visiting research assistant professor at University of California Davis, and 16 years at Florida State University (now a professor in the Mathematics department). Mark Sussman's research specializes in numerical methods for deforming boundary problems with applications to multiphase flow. Mark Sussman has authored/co-authored many articles in refereed archival journals, served as a referee for articles submitted to archival journals in the fields of mathematics, engineering, biology, chemistry, and computer science, and has served on many proposal review panels.