Grid cell volume control with an adaptive grid generator
Applied Mathematics and Computation
A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection
Computer Methods in Applied Mechanics and Engineering
Reconstructing volume tracking
Journal of Computational Physics
A method for capturing sharp fluid interfaces on arbitrary meshes
Journal of Computational Physics
A new volume of fluid advection algorithm: the stream scheme
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A quadtree adaptive method for simulating fluid flows with moving interfaces
Journal of Computational Physics
A volume of fluid method based on multidimensional advection and spline interface reconstruction
Journal of Computational Physics
Journal of Computational Physics
Numerical simulation of melting in two-dimensional cavity using adaptive grid
Journal of Computational Physics
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Journal of Computational Physics
Review of code and solution verification procedures for computational simulation
Journal of Computational Physics
A new interface tracking method: The polygonal area mapping method
Journal of Computational Physics
Short Note: Analytical and geometrical tools for 3D volume of fluid methods in general grids
Journal of Computational Physics
Front tracking with moving-least-squares surfaces
Journal of Computational Physics
Journal of Computational Physics
A Newton-Krylov Solver for Remapping-Based Volume-of-Fluid Methods
SIAM Journal on Scientific Computing
Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids
Journal of Computational Physics
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This paper presents a new variant of the volume-of-fluid (VOF) color function C advection algorithm based on the piecewise linear interface construction (PLIC) method suitable for use on general moving grids. From several existing methods for reconstructing the linear interface we adopted the least squares volume-of-fluid interface reconstruction algorithm (LVIRA) which can be easily implemented on general grids. The distinguishing step in the advection algorithm that takes into account the grid movement is the construction of the donating region containing the fluid passing through corresponding cell-faces in a single time-step. The donating regions are constructed utilizing fluid velocity in cell corners relative to grid (corner) velocities. The method is conservative as it complies with the space conservation law (SCL) and requires a proper definition of the grid velocities and fluxes due to the grid movement. The accuracy of the presented advection algorithm is assessed with standard test cases. It is comparable with other PLIC based algorithms on fixed grids, while the applicability on adaptive moving grids enables a considerable reduction in the number of grid cells.