A hybrid variational front tracking-level set mesh generator for problems exhibiting large deformations and topological changes

Abstract

We present a method for generating 2-D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level set method to guide the change of topology of the domain mesh. This is followed by an optimization procedure, using a variational formulation of active contours, that seeks to improve boundary mesh conformity to the zero level contour of the level set function. Our method is advantageous for Arbitrary-Lagrangian-Eulerian (ALE) type methods and directly allows for using a variational formulation of the physics being modeled and simulated, including the ability to account for important geometric information in the model (such as for surface tension driven flow). Furthermore, the meshing procedure is not required at every time-step and the level set update is only needed during a topological change. Hence, our method does not significantly affect computational cost.

Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions

“…The computational time of TO-1(10) is less than one fifth of that of GB(10). The L 2 -norm of error of TO-1(10) is also smaller than GB (10). As expected, the TO-2(10) case is more accurate, but takes more time than TO-1(9).…”

“…Figs. 8(a)-(d) show the droplet shape at the maximum deformation (t = T /2) based on the gradient-based refinement with four different levels, from GB(7) to GB (10), where the quantity within the parentheses stands for the interfacial level. The unphysical rupture of the tail disappears with increasing refinement level.…”

“…Mesh splicing operations were required to simulate pinch-off and coalescing events that involve topological changes of interfaces. Nochetto and Walker [10] employed a method capable of detecting imminent topological changes by means of distance functions and shape skeletons. Mesh was adaptively refined until no triangle intersects either the shape skeleton or the interface.…”

A Mixed Finite Element Method for EWOD That Directly Computes the Position of the Moving Interface

“…We chose E in order to drive the five droplets toward each other. Once the droplets are sufficiently close, we stop the simulation and use a hybrid level set/mesh generation method to enable the topological change [29,39]; this happens during one time-step and creates a new domain Ω. We then restart the simulation using Ω as the initial domain with initial velocity obtained by interpolating from the previous domain.…”

A flexible level-set approach for tracking multiple interacting interfaces in embedded boundary methods

“…Furthermore, simply advecting the surface mesh points with their respective local velocity can lead to tangling and self-intersection of the mesh [31]. Especially when multiple interfaces move independently and interact with each other, situations will occur that are difficult to deal with in explicit surface representations, such as overlaps of the respective surface meshes and topological changes [32][33][34]. Finally, although the use of component based geometry, i.e., a complex geometry which is composed of different separate components that are allowed to intersect and perform relative motion, is possible, this comes at the expense of added complexity and costs, since the reconstruction algorithm must be able to extract the relevant part of the geometry, i.e., the wetted surface [35,36].…”