This project explored the solution of differential distance function equations on unstructured moving and overset meshes. Flow solutions using such grids are increasingly common. However, robust mesh generation still presents a significant challenge. This is especially so if use is made of hexahedral cells and the higher numerical fidelity that they provide. The differential equations explored will include the hyperbolic Eikonal, Hamilton-Jacobi and elliptic Poisson. Especial attention will be paid to the economical and accurate solution of these equations on moving, unstructured over-set grids with mixed element topologies using finite element, finite volume & boundary element methods.