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A new algorithm for volume tracking which is based on the concept of flux‐corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction‐split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the new scheme against well‐known existing 2D finite volume techniques is undertaken. A series of progressively more difficult advection tests is used to test the accuracy of each scheme and it is seen that simple advection tests are inadequate indicators of the performance of volume‐tracking methods. A straightforward methodology is presented that allows more rigorous estimates to be made of the error in volume advection and coupled volume and momentum advection in real flow situations. The volume advection schemes are put to a final test in the case of Rayleigh–Taylor instability. © 1997 by CSIRO.

A numerical technique (FGVT) for solving the time-dependent incompressible Navier -Stokes equations in fluid flows with large density variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise-linear interface reconstruction on a grid twice as fine as the velocity-pressure grid. It also uses a special flux-corrected transport algorithm for momentum advection, a multigrid algorithm for solving a pressure-correction equation and a surface tension algorithm that is robust and stable. In principle, the method conserves both mass and momentum exactly, and maintains extremely sharp fluid interfaces. Applications of the numerical method to prediction of two-dimensional bubble rise in an inclined channel and a bubble bursting through an interface are presented.where the symbols A and D refer to the advective and diffusive operators respectively (discussed below). 3. Calculate the pressure correction, lP, from the discrete form of the Helmholtz equation, 9 · 1 z n + 1 9lP = 1 lt 9 · U*,

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Numerical simulations have been used to investigate the flow regimes resulting from the impact of a 2.9 mm water drop on a deep water pool at velocities in the range 0.8–2.5 m/s. The results were used to identify the conditions leading to the formation of vortex rings, entrapment of a bubble during cavity collapse and the formation of vertical Rayleigh jets. Bubble entrapment and the associated growth of a thin high speed jet were shown to be the result of a capillary wave that propagates down the walls of the crater resulting from drop impact. Although the existence of a capillary waves is a necessary condition for bubble entrapment, bubbles will only occur when the wave speed and maximum crater size is such that the wave reaches the bottom of the crater before collapse has resulted in the formation of a thick Rayleigh jet. Simulations also clarified the conditions for which drop impact leads to axi-symmetric vortex rings. Results not reported previously, include the observation that a single drop can produce multiple vortex rings and that vortex rings can occur for conditions that lead to broad Rayleigh jets. Based on these results, it was concluded that the formation of vortex rings depends on the time at which vorticity is generated and the nature of its subsequent transport.

A numerical technique (FGVT) for solving the time‐dependent incompressible Navier–Stokes equations in fluid flows with large density variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise‐linear interface reconstruction on a grid twice as fine as the velocity–pressure grid. It also uses a special flux‐corrected transport algorithm for momentum advection, a multigrid algorithm for solving a pressure‐correction equation and a surface tension algorithm that is robust and stable. In principle, the method conserves both mass and momentum exactly, and maintains extremely sharp fluid interfaces. Applications of the numerical method to prediction of two‐dimensional bubble rise in an inclined channel and a bubble bursting through an interface are presented. © 1998 John Wiley & Sons, Ltd.

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