VOF with center of mass and Lagrangian particles (VCLP): a surface tracking and advection method for incompressible fluids

A novel surface tracking, and advection algorithm for incompressible fluid flows in two and three dimensions is presented. This method based on the volume-of-fluid (VOF) method, is named VOF-with-center-of-mass-and-Lagrangian-particles (VCLP), and it uses spatially and temporally localized Lagrangian particles (LPs) inside a finite volume framework. The fluid surface is recaptured and reconstructed piecewise using the mean slope and curvature. The fluid mass inside each cell is discretized spatially by LPs and distributed as blue noise. LPs are then advected cell by cell with a choice of two different advection schemes in time using interpolated velocity and approximated acceleration fields. VCLP continuously tracks the center of mass of the fluid parcels in the Lagrangian way and this helps to reduce the errors due to numerical acceleration that results from lack of information to reconstruct the interface accurately. VCLP’s performance is evaluated using standard benchmark tests in 2D and 3D such as translation, single vortex, deformation, and Zalesak’s tests from the literature. VCLP is applied to TSUNAMI2D, a 2D Navier–Stokes model to simulate shoaling and breaking of waves.