Volume Tracking Algorithm Research Articles

Controls on rapid supraglacial lake drainage in West Greenland: an Exploratory Data Analysis approach

ABSTRACTThe controls on rapid surface lake drainage on the Greenland ice sheet (GrIS) remain uncertain, making it challenging to incorporate lake drainage into models of GrIS hydrology, and so to determine the ice-dynamic impact of meltwater reaching the ice-sheet bed. Here, we first use a lake area and volume tracking algorithm to identify rapidly draining lakes within West Greenland during summer 2014. Second, we derive hydrological, morphological, glaciological and surface-mass-balance data for various factors that may influence rapid lake drainage. Third, these factors are used within Exploratory Data Analysis to examine existing hypotheses for rapid lake drainage. This involves testing for statistical differences between the rapidly and non-rapidly draining lake types, as well as examining associations between lake size and the potential controlling factors. This study shows that the two lake types are statistically indistinguishable for almost all factors investigated, except lake area. Thus, we are unable to recommend an empirically supported, deterministic alternative to the fracture area threshold parameter for modelling rapid lake drainage within existing surface-hydrology models of the GrIS. However, if improved remotely sensed datasets (e.g. ice-velocity maps, climate model outputs) were included in future research, it may be possible to detect the causes of rapid drainage.

A Lagrangian-Eulerian Volume-Tracking with Linearity-Preserving Interface Reconstruction

This article presents a linearity-preserving volume-tracking algorithm for two-phase flow based on volume fraction remapping. The approach followed here does not deal with edge flux and corner flux computation or with corner flux correction typical of unsplit Eulerian advection. The method discussed is a Lagrangian-Eulerian advection scheme (LEAS) which is CFL condition-independent, in contrast to most of the unsplit Eulerian advection algorithms. Also, the scheme is equally applicable on general polygonal grids. The method works on the assumption that fluid content remains constant inside a stream tube generated between a Eulerian cell and a Lagrangian precell. The Lagrangian precell is obtained by back tracking of cell vertices in time. Volume fraction remapping is performed by a series of polygon intersections between a Lagrangian precell and vertex-connected neighbor cell fluid polygons. The fluid polygons are obtained from interface reconstruction. The volume fraction inconsistencies are removed by a conservative volume-fraction repair algorithm. Since interface reconstruction is also an integral part of the overall volume tracking algorithm, details of the same are presented for the sake of completeness. Overall volume tracking error is due solely to approximate interface reconstruction, while the scheme is derived naturally from the fact that volume inside a stream tube remains constant. LEAS performs better compared to the existing unsplit algorithms for the same interface reconstruction.

The global embedded interface formulation for interfacial mass transfer within a volume tracking framework

Interfacial flow with mass transfer is particularly challenging to compute because the position of the interface between the fluids and the interface physics needs to be predicted as part of the solution of the flow equations. In addition, the discontinuity in fluid density, viscosity and species concentration at the interface present additional numerical challenges. In this work, we extend our balanced-force volume-tracking algorithm for modeling interfacial flow with surface tension force [10] to include mass transfer. We propose a global embedded interface formulation to model the interfacial conditions of the species concentration at an interface in thermodynamic equilibrium. To verify our formulation, we perform simulations of a pure diffusion problem with species concentration discontinuity at the interface. Then we present two and three-dimensional simulations of droplets rising by buoyancy with mass transfer.

Piecewise linear volume tracking in spherical coordinates

We present a detailed description of a geometric piecewise linear (PLIC) volume tracking algorithm for spherical coordinates, which is a component of a flow solver being developed to study contact line dynamics on small particles. Tests demonstrate the robustness of the method, and include reconstructions of various geometries, and tests of the split advection algorithm. Reconstruction is shown to be first-order accurate; errors associated with the advection algorithm decrease at a rate greater than first-order. Finally, the paper demonstrates the implementation of a contact angle model.

A numerical method for interface reconstruction of triple points within a volume tracking algorithm

A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a triple point is described as the minimum of a constrained minimization problem inside an interfacial cell of the discretization. For given volume fractions of materials in the cell, an interior-point/Newton method is used for the reconstruction of the local geometry and the localization of the triple point. Initialization of the Newton method is performed with a derivative-free algorithm. Numerical results are presented for static and pure advection cases to illustrate the efficiency and robustness of the algorithm.

A 3D unsplit-advection volume tracking algorithm with planarity-preserving interface reconstruction

A new volume tracking method is introduced for tracking interfaces in three-dimensional (3D) geometries partitioned with orthogonal hexahedra. The method approximates interface geometries as piecewise planar, and advects volumes in a single unsplit step using fully multidimensional fluxes that have their definition based in backward-trajectory remapping. By using multidimensional unsplit advection, the expense of high-order interface reconstruction is incurred only once per timestep. Simple departures from strict backward-trajectory remapping remove any need for consideration of volume computations involving shapes consisting of non-planar ruled surfaces. Second-order accuracy of the method is demonstrated even for vigorous 3D deformations.

A three-dimensional model of droplet impact and solidification

A three-dimensional model has been developed to simulate the fluid dynamics, heat transfer and phase-change that occur when a molten metal droplet falls onto a flat substrate. The model is an extension of one developed by Bussmann et al. [Phys. Fluids 11 (1999) 1406] and combines a fixed-grid control volume discretization of the fluid flow and energy equations with a volume-tracking algorithm to track the droplet free surface, and an improved fixed velocity method to track the solidification front. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at liquid–solid contact lines. The energy equations in both the liquid and solid portions of the droplet are solved using the Enthalpy method. Heat transfer within the substrate is by conduction alone. Thermal contact resistance at the droplet–substrate interface is included in the model. We studied the deposition of tin droplets on a stainless steel surface using both experiments and numerical simulations. The results of two different scenarios are presented: the normal impact of a 2.7 mm tin droplet at 1 m/s, and of the oblique impact of a 2.2 mm tin droplet at 2.35 m/s onto a surface inclined at 45° to the horizontal. Images obtained from numerical model were compared with experimental photographs and found to agree well.

Modélisation numérique du déferlement plongeant

ABSTRACT Wave breaking is simulated using the Navier-Stokes equations and the volume tracking algorithm PLIC-VOF. The method is first validated on the case of non linear wave propagation on flat bottom. The plunging motion of a sinusoidal wave of large initial steepness is next studied. The characteristics of the wave up to the impact are found to be well described by the method. First results obtained after the impact encourage us to go on in this direction.

On a three-dimensional volume tracking model of droplet impact

A three-dimensional model has been developed of droplet impact onto asymmetric surface geometries. The model is based on RIPPLE, and combines a fixed-grid control volume discretization of the flow equations with a volume tracking algorithm to track the droplet free surface. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at the contact line. The results of two scenarios are presented, of the oblique impact of a 2 mm water droplet at 1 m/sec onto a 45° incline, and of a similar impact of a droplet onto a sharp edge. Photographs are presented of such impacts, against which the numerical results are compared. The contact angle boundary condition is applied in one of two ways. For the impact onto an incline, the temporal variation of contact angles at the leading and trailing edges of the droplet was measured from photographs. This data is applied as a boundary condition to the simulation, and an interpolation scheme proposed to evaluate contact angles between the leading and trailing edges. A simpler model is then proposed, for contact angle as a function of contact line velocity, and applied to both geometries. The model requires values of only two contact angles, at a rapidly advancing and a rapidly receding contact line. Simulation results compare well with photographic data.

Finite-element development for two-dimensional multiple-interface phase-change problems

A three-dimensional model has been developed to simulate the fluid dynamics, heat transfer and phase-change that occur when a molten metal droplet falls onto a flat substrate. The model is an extension of one developed by Bussmann et al. [Phys. Fluids 11 (1999) 1406] and combines a fixed-grid control volume discretization of the fluid flow and energy equations with a volume-tracking algorithm to track the droplet free surface, and an improved fixed velocity method to track the solidification front. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at liquid–solid contact lines. The energy equations in both the liquid and solid portions of the droplet are solved using the Enthalpy method. Heat transfer within the substrate is by conduction alone. Thermal contact resistance at the droplet–substrate interface is included in the model. We studied the deposition of tin droplets on a stainless steel surface using both experiments and numerical simulations. The results of two different scenarios are presented: the normal impact of a 2.7 mm tin droplet at 1 m/s, and of the oblique impact of a 2.2 mm tin droplet at 2.35 m/s onto a surface inclined at 45° to the horizontal. Images obtained from numerical model were compared with experimental photographs and found to agree well.