A grid based particle method for moving interface problems

Abstract

We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for the particles on the interface. It also renders neighborhood information among the meshless particles for local reconstruction of the interface. The resulting algorithm, which is based on Lagrangian tracking using meshless particles with Eulerian reference grid, can naturally handle/control topological changes. Moreover, adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad/oct-tree data structure. Extensive numerical examples are presented to demonstrate the capability of our new algorithm.

A grid based particle method for evolution of open curves and surfaces

“…In [17], we represent the interface by meshless particles which are associated to an underlying Eulerian mesh. Each sampling particle on the interface is chosen to be the closest point from each underlying grid point in a small neighborhood of the interface.…”

“…Due to the availability of both Eulerian information, i.e., reference to the underlying mesh, and Lagrangian information of particles, the meshless representation allows us to detect collision of different interfaces and to control topological changes easily. For more details, we refer interested readers to [17] for each of the above procedures.…”

“…In a recent work [17], we proposed a novel grid based particle method to represent and track interface motion. In our approach the interface is represented by meshless, i.e., no triangulation or parametrization, Lagrangian particles which are associated to an underlying uniform or an adaptive Eulerian mesh.…”

“…The goal of this paper is to generalize the techniques in [17] [21]. One approach was the work of [23] for modeling spiral crystal growth.…”

“…Similar to our representation in [17], the vector level set method [25] modeled propagating crack using also closest points from an underlying fixed mesh. However, their motion law was imposed only at the tip of an open curve.…”