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Volume of fluid method
About: Volume of fluid method is a research topic. Over the lifetime, 5338 publications have been published within this topic receiving 116760 citations.
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11 May 1998
TL;DR: The Navier-Stokes equation is derived from the advection-diffusion equation as discussed by the authors, and the Navier Stokes equation derived quantities are derived from weak operators some element matrices and projection methods.
Abstract: The advection-diffusion equation the Navier-Stokes equation derived quantities. Appendices: weak operators some element matrices and projection methods.
324 citations
TL;DR: A numerical model NEWTANK (Numerical Wave TANK) has been developed to study three-dimensional (3-D) non-linear liquid sloshing with broken free surfaces to solve the spatially averaged Navier-Stokes equations for two-phase flows.
307 citations
TL;DR: In this article, a volume-of-fluid scheme with piecewise linear interface construction is proposed to implement the contact angle condition, where the body forces are treated as a continuous body force, computed from numerical derivatives of a smoothed volume of fluid function.
302 citations
TL;DR: In this paper, the enlargement of a lens-shaped cavity lying in a plane of cleavage between two elastic half spaces and filling with viscous fluid from a source on the axis of symmetry is considered.
Abstract: The enlargement of a lens-shaped cavity lying in a plane of cleavage between two elastic half spaces and filling with viscous fluid from a source on the axis of symmetry is considered. The internal flow is modelled by lubrication theory, which gives a nonlinear partial differential equation connecting the pressure to the cavity shape, and the same two quantities are also related by the singular integral equation of linear elasticity. If the total volume of fluid Q ( t ) in the cavity at time t is proportional either to t α or to exp (α t ) the resulting boundary value problem can be reduced to a self-similar form in which time does not appear explicitly. The solution in non-dimensional terms depends on a single parameter, which may be interpreted as the stress-intensity factor K at the tip. Calculations have been made for the two-dimensional version of the problem for a range of values of α and for a range of stress intensities. The numerical method is to expand the cavity height in a Chebyshev series, the coefficients being found by a nonlinear optimization technique to yield a least squares fit to the Reynolds equation. These lead to expressions for the rate of cavity growth and other quantities of physical interest.
298 citations
TL;DR: In this paper, a cell volume fraction field is obtained by integrating the advected area underneath the interface line-segment and a criterion is developed for identifying the line segment orientation by inspecting the cell volume fractions.
285 citations