Changing Time History in Moving Boundary Problems

Space-Time Meshing for Two-Dimensional Moving Boundary Problems

A new meshing strategy for two-dimensional space-time moving boundary methods is presented. The method breaks the space-time domain into time slabs, and tesselates each sequentially. Within each time slab, the mesh is generated by extruding the lower time plane, moving the boundary, adding and removing vertices near the boundary, and smoothing. Unlike other strategies, topological changes to th...

Moving boundary problems on Earth’s surface

In a moving boundary problem one or more of the domain boundaries is an unknown function of time. The classic moving boundary problem, the Stefan problem, is related to the tracking of a sharp liquid/solid front during the melting of ice. A major societal problem of our time is the current rapid rate of degradation of Earth environments and resources through climate change and other anthropogen...

Moving Boundary Problems with Nonlinear Diffusion

Moving boundary problems governed by anomalous diffusion.

Anomalous diffusion can be characterized by a mean-squared displacement 〈x(2)(t)〉 that is proportional to t(α) where α≠1. A class of one-dimensional moving boundary problems is investigated that involves one or more regions governed by anomalous diffusion, specifically subdiffusion (α<1). A novel numerical method is developed to handle the moving interface as well as the singular history kernel...

An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems