Automatic Mesh Motion for the Unstructured Finite Volume Method

Moving-mesh unstructured Finite Volume Method (FVM) is a good candidate for tackling flow simulations where the shape of the domain changes during the simulation or represents a part of the solution. For efficient and user-friendly approach to the problem, it is necessary to automatically determine the point positions in the mesh, based on the prescribed boundary motion. In this paper, we present a vertex-based unstructured mesh motion solver designed to work with the movingmesh FVM. Motion is determined by solving the Laplace equation with variable diffusion on mesh points, using a tetrahedral decomposition of polyhedral cells. Cell decomposition and discretisation guarantees that an initially valid mesh remains geometrically valid for arbitrary boundary motion. Efficiency of the method is preserved by careful discretisation and the choice of iterative solvers, allowing the motion solver to efficiently couple with the FVM flow solver. This combination is tested on two free surface tracking flow simulations, including the simulation of free-rising air bubbles in water.