A computational Lagrangian–Eulerian advection remap for free surface flows

A VOF‐based algorithm for advecting free surfaces and interfaces across a 2‐D unstructured grid is presented. This algorithm is based on a combination of a Computational Lagrangian–Eulerian Advection Remap and the Volume of the Fluid method (CLEAR‐VOF). A set of geometric tools are used to remap the advected shape of the volume fraction from one cell onto the Eulerian fixed unstructured grid. The geometric remapping is used to compute the fluxes onto a group of neighbouring cells of the mesh. These fluxes are then redistributed and corrected to satisfy the conservation of mass. Here, we present methods for developing identification algorithms for surface cells and incorporating them with CLEAR‐VOF. The CLEAR‐VOF algorithm is then tested for translation of several geometries. It is also incorporated in a finite element based flow solver and tested in a laminar flow over a broad‐crested weir and a turbulent flow over a semi‐circular obstacle.