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SUMMARYA multidimensional advection scheme in 3D based on the use of face-matched flux polyhedra to integrate the volume fraction evolution equation is proposed. The algorithm tends to reduce the formation of 'over/undershoots' by alleviating the over/underlapping of flux polyhedra, thus diminishing the need to use local redistribution algorithms. The accuracy and efficiency of the proposed advection algorithm, which are analyzed using different tests with prescribed velocity field, compare well with other multidimensional advection methods proposed recently. The algorithm is also applied, in combination with a Navier-Stokes solver, to reproduce the impact of a water droplet falling through air on a pool of deep water. The interfacial curvature is calculated using a height-function technique with adaptive stencil adjustment, which provides improved accuracy in regions of low grid resolution. The comparison of the numerical results with experimental results shows a good degree of agreement.

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SUMMARYA local level set algorithm for simulating interfacial flows described by the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations are solved using a finitedifference discretization on a Cartesian grid and a second-order approximate projection method. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid, which is reconstructed every time step and refined using a simple uniform cell-splitting operation within the band. Instabilities at the border of the narrow band are avoided by smoothing the level set function in the outer part of the band. The influence of different PDE-based reinitialization strategies on the accuracy of the results is investigated. The ability of the proposed method to accurately compute interfacial flows is discussed using different tests, namely the advection of a circle of fluid in two different time-reversed vortex flows, the advection of Zalesak's rotating disk, the propagation of small-amplitude gravity and capillary waves at the interface between two superposed viscous fluids in deep water, and a classical test of Rayleigh-Taylor instability with and without surface tension effects. The interface location error and area loss for some of the results obtained are compared with those of a recent particle level set method.

SUMMARYA new interface reconstruction method in 3D is presented. The method involves a conservative levelcontour reconstruction coupled to a cubic-Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second-order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required.

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