Automatic mesh motion for the unstructured finite volume method

The moving-mesh unstructured Finite Volume Method (FVM) provides a capability of tackling flow simulations where the domain shape changes during the simulation. In such cases, the computational mesh needs to adapt to the time-varying shape of the domain and preserve its validity and quality. In this paper, we present a vertex-based unstructured mesh motion solver with the polyhedral cell support which calculates the internal point motion based on the prescribed motion of the boundary. The performance of the method is preserved through the choice of decomposition of polyhedral cells, the bounded discretisation and the use of iterative solvers. A mechanism for minimising mesh distortion through variable stiffness is proposed and tested on a simple deformation case, showing a marked improvement on previous attempts. Finally, the moving mesh solver is used with an unstructured moving mesh FVM algorithm to simulate a free-rising air bubble in water.