In this paper, noniterative interface reconstruction algorithms for volume of fluid (VOF) method are presented. Analytical expressions are derived to determine the coefficients of the curve to achieve a noniterative reconstruction procedure. Static interface reconstruction tests of standard geometries like circle and ellipse are performed. The noniterative algorithm based on Piecewise Linear Interface Calculation from an earlier work is found to reconstruct the VOF value within machine tolerance. Two piecewise continuous algorithms are also proposed in this work, which ensures C0 continuity. The first algorithm, namely, Piecewise Continuous Linear Interface Calculation (PCLIC), uses piecewise continuous linear segments to approximate the interface. The second algorithm uses piecewise continuous quadratic curve and is named as Piecewise Continuous Quadratic Interface Calculation. PCLIC is seen to achieve machine tolerance in reconstructing the VOF value. Piecewise Continuous Quadratic Interface Calculation is found to give a more accurate estimate of the length of the interface than Piecewise Linear Interface Calculation and PCLIC. © 2013 John Wiley &amp; Sons, Ltd.

Shamit Bakshi

Department of Mechanical Engineering

Analytical expressions

INTERFACE RECONSTRUCTION

NON-ITERATIVE ALGORITHMS

PIECEWISE LINEAR INTERFACE CALCULATIONS

PIECEWISE-CONTINUOUS

QUADRATIC CURVES

RECONSTRUCTION PROCEDURE

Volume of fluid method

Piecewise linear techniques

Algorithms

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

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IIT Madras

International Journal for Numerical Methods in Fluids

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function (C0) and derivative (C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water. © 2009 Elsevier Inc. All rights reserved.

Journal of Computational Physics

A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

Computers & Structures

Estimating curvature from volume fractions

Second-order accurate volume-of-fluid algorithms for tracking material interfaces

A volume of fluid method based on multidimensional advection and spline interface reconstruction

A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles

Noniterative interface reconstruction algorithms for volume offluid method

Journal	International Journal for Numerical Methods in Fluids
ISSN	02712091
Open Access	No