Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement

Abstract

SUMMARYA novel numerical scheme is developed by coupling the level set method with the adaptive mesh reÿnement in order to analyse moving interfaces economically and accurately. The ÿnite element method (FEM) is used to discretize the governing equations with the generalized simpliÿed marker and cell (GSMAC) scheme, and the cubic interpolated pseudo-particle (CIP) method is applied to the reinitialization of the level set function. The present adaptive mesh reÿnement is implemented in the quadrangular grid systems and easily embedded in the FEM-based algorithm. For the judgement on renewal of mesh, the level set function is adopted as an indicator, and the threshold is set at the boundary of the smoothing band. With this criterion, the variation of physical properties and the jump quantity on the free surface can be calculated accurately enough, while the computation cost is largely reduced as a whole. In order to prove the validity of the present scheme, two-dimensional numerical simulation is carried out in collapse of a water column, oscillation and movement of a drop under zero gravity. As a result, its e ectiveness and usefulness are clearly shown qualitatively and quantitatively. Among them, the movement of a drop due to the Marangoni e ect is ÿrst simulated e ciently with the present scheme.

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).…”

“…Option 3 above which has been used in a number of recent studies [28,30,8,36,31,9,38,64,33,39] is simple to implement within a vof framework but does not make full use of adaptivity. The total cpu time ( ≈ 6,000 timesteps) for the simulation of Figures 19-21, 25 is about three hours on a 2.5 GHz 32 bits Intel Pentium processor.…”

“…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].…”

“…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].…”

Superficial transportation model using finite volume method

“…There are algorithms which rely on the use of particles to track desired variable or flow property. Some of the examples are the MAC method [28] and its several variants: SMAC [29] (simplified marker and cell), GENSMAC [30] (general domains simplified marker and cell), GSMAC [31] (generalized simplified marker and cell).…”