Data Transfer and Interface Propagation in Multicomponent Simulations

This thesis addresses various computational problems arising from interfacing software components in three-dimensional multicomponent simulations. Typically, the computational domain for each physical component in such a simulation is discretized using a volume mesh, and the meshes for adjacent domains abut each other at a common interface surface. In general, the two discretizations of such an interface from different components differ both geometrically and combinatorially, and data must be exchanged between these disparate interface meshes. We address the problems of correlating disparate interface meshes and transferring data between them in a numerically accurate and physically conservative manner. In many cases, the interface evolves due to various processes, such as deformation, burning, or erosion, and we also consider the problem of propagating the interface surface dynamically as the components evolve over time. We first consider two variants of correlating nonmatching interface meshes. We present two efficient algorithms for the simpler one, mesh association , which associates vertices from one mesh with facets of another mesh. We then consider a more general variant, mesh overlay, which constructs a common refinement, that is, a finer mesh whose polygons subdivide the polygons of the input meshes. Our algorithm constructs a minimal common refinement in linear time using a conforming homeomorphism , and achieves robustness through the intersection principle to resolve any inconsistencies due to numerical errors. Second, we develop accurate, conservative, and efficient data transfer algorithms for exchanging data between interface meshes based on the common refinement. We analyze two classes of approaches, point-wise interpolation and weighted residual methods. The analyses and evaluation of existing methods lead us to a more advanced formulation and an optimal discretization for weighted residual methods. We demonstrate significant advantages of our methods, propose treatments for inconsistencies in interface geometries, and develop an optimally scalable parallel implementation. This thesis also considers the interface propagation problem, formulated with an entropy-satisfying Huygens' principle . We introduce the concepts of prevoid sets and critical times of an evolving interface, and develop a new approach based on these concepts to resolve singularities and topological changes in the interface. This problem is addressed in two dimensions, and a three-dimensional generalization is outlined.