Editorial: Moving boundary problems in multi-physics coupling processes

Coupling Requirements for Well Posed and Stable Multi-physics Problems

Abstract. We discuss well-posedness and stability of multi-physics problems by studying a model problem. By applying the energy method, boundary and interface conditions are derived such that the continuous and semi-discrete problem are well-posed and stable. The numerical scheme is implemented using high order finite difference operators on summation-by-parts (SBP) form and weakly imposed boun...

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...

Coupling Algorithms for Partitioned Multi-Physics Simulations

Partitioned coupling approaches are an important tool in order to achieve a decent time-to-solution for multi-physics problems with more than two physical fields or changing combinations of fields. We study different approaches to deduce coupling schemes for partitioned multi-physics scenarios, by means of a simple, but yet challenging fluid-structure-fluid model problem. To our knowledge, this...