Analysis of the Interface Tracking Errors

Journal of Computational Physics, 2007

A Volume Tracking (VT) and a Front Tracking (FT) algorithm are implemented and compared for locating the interface between two immiscible, incompressible, Newtonian fluids in a tube with a periodically varying, circular cross-section. Initially, the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube (core fluid) and the other one surrounds it (annular fluid). A constant pressure gradient sets them in motion. With both VT and FT, a boundary-fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry. The surface tension force is approximated using the continuous surface force method. All terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and onesided forward finite differences in time. In each time step, the incompressibility condition is enforced by a transformed Poisson equation, which is linear in pressure. This equation is solved by either direct LU decomposition or a Multigrid iterative solver. When the two fluids have the same density, the former method is about 3.5 times faster, but when they do not, the Multigrid solver is as much as 10 times faster than the LU decomposition. When the interface does not break and the Reynolds number remains small, the accuracy and rates of convergence of VT and FT are comparable. The wellknown failure of centered finite differences arises as the Reynolds number increases and leads to non-physical oscillations in the interface and failure of both methods to converge with mesh refinement. These problems are resolved and computations with Reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third-order upwind differences using Lagrangian Polynomials. When the volume of the core fluid or the Weber number decrease, increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid, the FT method converges faster with mesh refinement than the VT method and upwinding may be required. Finally, examining the generation of spurious currents around a stationary ''bubble'' in the tube for Ohnesorge numbers between 0.1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when VT is applied, whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when FT is applied.

Journal of Computational Physics, 2008

A new, fully three-dimensional, vortex-in-cell method designed to follow the unsteady motion of inviscid vortex sheets with or without small (Boussinesq) density discontinuities is presented. As is common in front-tracking methods, the vortex sheet is described by a moving, unstructured mesh consisting of points connected by triangular elements. Each element carries scalar-valued circulations on its three edges, which can be used to represent any tangent vector value and in the present method represent the element's vorticity. As the interface deforms, nodes and elements are added and removed to maintain the resolution of the sheet and of the vortex sheet strength. The discretization and remeshing methods allow automatic, near-perfect conservation of circulation despite repeated stretching and folding of the interface. Results are compared with previous experiments and simulations. Similarities are observed between the present simulations and experiments of a vortex ring impacting a wall.

1997

Motivated by the need for three-dimensional methods for interface calculations that can deal with topology changes, we describe a numerical scheme, built from a volume-of-fluid interface tracking technique that uses a piecewise-linear interface calculation in each cell. Momentum balance is computed using explicit finite volume/finite differences on a regular cubic grid. Surface tension is implemented by the continuous surface stress or continuous surface force method. Examples and verifications of the method are given by comparing simulations to analytical results and experiments, for sedimenting droplet arrays and capillary waves at finite Reynolds number. In the case of a pinching pendant drop, both three-dimensional and axisymmetric simulations are compared to experiments. Agreement is found both before and after the reconnections.

2017

Two-phase and multi-phase flows are common flow types in fluid mechanics engineering. Among the basic and applied problems of these flow types, two-phase parallel flow is the one that two immiscible fluids flow in the vicinity of each other. In this type of flow, fluid properties (e.g. density, viscosity, and temperature) are different at the two sides of the interface of the two fluids. The most challenging part of the numerical simulation of two-phase flow is to determine the location of interface accurately. In the present work, a coupled interface tracking algorithm is developed based on Arbitrary Lagrangian-Eulerian (ALE) approach using a cell-centered, pressure-based, coupled solver. To validate this algorithm, an analytical solution for fully developed two-phase flow in presence of gravity is derived, and then, the results of the numerical simulation of this flow are compared with analytical solution at various flow conditions. The results of the simulations show good accurac...

34th Aerospace Sciences Meeting and Exhibit, 1996

Solution algorithms are presented for tracking interfaces with piecewise linear (PUC) volume-of-fluid (VOF) methods on fixed (Eulerian) two-dimensional (2-D) structured and three-dimensional (3-D) structured and unstructured grids. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify and present solutions to the basic geometric functions needed for interface reconstruction and volume fluxing, and provide detailed algorithm templates for modem 2-D and 3-D PUC VOF interface tracking methods. We discuss somekey outstanding issues for PUC VOF methods. namely the method used for time integration of fluid volumes (operator splitting, unsplit, Runge-Kutta, etc.) and the estimation of interface normals. We also present our latest developments in the continuum surface force (CSF) model for surface tension. namely extension to 3-D and variable surface tension effects. We identify and focus on key outstanding CSF model issues that become especially critical on fine meshes with high density ratio interfacial flows, namely the surface delta function approximation, the estimation of interfacial curvature, and the continuum surface force scaling and/or smoothing model. Numerical results in two and three dimensions are used to illustrate the properties of these methods.

2006

In this study, an interface-tracking method, NS-PFM, combining Navier-Stokes (NS) equations with a phase-field model (PFM) is applied to an incompressible two-phase free surface flow problem at a high density ratio equivalent to that of an air-water system, for examining the computational capability. Based on the Cahn-Hilliard free energy theory, PFM describes an interface as a finite volumetric zone across which physical properties vary steeply but continuously. Surface tension is defined as an excessive free energy per unit area induced by local density gradient. Consequently, PFM simplifies the interface-tracking procedure on a fixed spatial grid without any elaborating techniques in conventional numerical methods. It was confirmed through the numerical simulation that (1) the NS-PFM conducts self-organizing reconstruction of the interface with a certain thickness using volume flux driven by chemical potential gradient and (2) predicted collapse of two-dimensional liquid column in a gas under gravity agreed well with available data.

Scientia Iranica

One of the most powerful methods to implement the free surface is the Volume Of Fluid (VOF). In this study, an algorithm is developed, which includes an implicit pressure based method (SIMPLE) with a staggered grid and a Lagrangian propagation VOF method. Based on this algorithm, a computer code is generated and a cavity with a free surface and two test cases of dam-breaking problems are examined and, then, the e ect of uid sloshing on a near w all is also analyzed and a time history of the normal force on the wa l l i s p resented. The results showgood agreement with experimental and other computational results. 2. No redistribution of the surface markers is necessary when they are stretched by the ow and no special 132 A.H. Nikseresht, M.M. Alishahi and H. Emdad

2022

We propose a novel class of Edge-Based Interface-Tracking (EBIT) methods in the field of multiphase flows for advecting the interface. The position of the interface is tracked by marker points located on the edges of the underlying grid, making the method flexible with respect to the choice of spatial discretization and suitable for parallel computation. In this paper we present a simple EBIT method based on two-dimensional Cartesian grids and on a linear interface representation.

Journal of Computational Physics, 1991

A method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described. The flow field is discretized by a conservative finite difference approximation on a stationary grid, and the interface is explicitly represented by a separate, unstructured grid that moves through the stationary grid. Since the interface deforms continuously, it is necessary to restructure its grid as the calculations proceed. In addition to keeping the density and viscosity stratification sharp, the tracked interface provides a natural way to include surface tension effects. Both two-and three-dimensional, full numerical simulations of bubble motion are presented.

SIAM Journal on Scientific Computing, 2002

Abstract. A front tracking method for inviscid gas dynamics is presented. The key construc-tions and algorithms used in the code are described and the interrelations between shock capturing, interface dynamics, computational geometry, grid construction, and parallelism ...