Level set calculations of the evolution of boundaries on a dynamically adaptive grid

Abstract

SUMMARYWe present a general algorithm for the study of the evolution of interfaces in growth processes based on the level set method, using the narrow band and the fast marching approximations, applied on a dynamically adaptive grid. A novel construction of a dynamical adaptive grid is presented. One important feature is that we establish a controllable ÿnite-width region of the highest resolution straddling the physically important boundary. This high-resolution stripe provides a better description of the important physical variables. An e cient and robust coupling of a hierarchical space description structure with the state-of-the-art level set method is established.

An accurate adaptive solver for surface-tension-driven interfacial flows

“…This is in contrast with many previous implementations of adaptive methods with vof or ls which restricted adaptivity to regions away from the interface (i.e. resolution along the interface was kept constant) [28,7,36,30,8,31,37,9,38,39,33,40]. A recent article by Malik et al [41] describes a two-dimensional quadtree implementation allowing variable resolution along the interface but their study is limited to the advection problem (not coupled to the momentum equation).…”

“…Numerical methods using an implicit representation of the interface such as Volume-OfFluid (vof) [1,2,3,4] or Levelset (ls) [5,6,7,8,9,10,11,12,13] can robustly and efficiently represent evolving, topologically complex interfaces. The accurate representation of surface tension within these methods is typically more delicate than for schemes using an explicit representation of the interface [14,15,16,17] and care must be taken to avoid any imbalance between discrete surface tension and pressure gradient terms [18,19,15,20,21,22,23].…”

“…For vof methods the accurate evaluation of the geometrical properties of the interface such as curvature is also an active research topic [24,21,25,23,26]. Finally dynamic mesh-adaptive methods can deal efficiently with phenomena involving a wide range of spatial scales [27,28,29,6,7,30,8,31,17,9,32,33,34].…”

Simulating water and smoke with an octree data structure

“…One difficulty with semi-Lagrangian methods for solving level set equations is that extreme mass loss (and thus visual artifacts) usually occurs, however [Enright et al 2004] recently showed that the particles in the particle level set method alleviate this difficulty. A quadtree structure for level set evolution was also proposed in [Sochnikov and Efrima 2003]. However, none of these authors considered level sets in the context of incompressible flows with interfaces such as water.…”

An octree-based solver for the incompressible Navier–Stokes equations with enhanced stability and low dissipation

“…Fast dynamic remeshing with octree grids makes them a natural choice for the simulation of moving interfaces and free surface flows, see, e.g., [5,6,7,8,9,10,11], octree grids became a standard tool in image processing [12].…”