  The generation of high-quality staggered unstructured grids is considered,
leading to the development of a new optimisation-based strategy designed to
construct weighted `Regular-Power' tessellations appropriate for co-volume type
numerical discretisation techniques. This new framework aims to extend the
conventional Delaunay-Voronoi primal-dual structure; seeking to assemble
generalised orthogonal tessellations with enhanced geometric quality. The
construction of these grids is motivated by the desire to improve the
performance and accuracy of numerical methods based on unstructured co-volume
type schemes, including various staggered grid techniques for the simulation of
fluid dynamics and hyperbolic transport. In this study, a new hybrid
optimisation strategy is proposed; seeking to optimise the geometry, topology
and weights associated with general, two-dimensional Regular-Power
tessellations using a combination of gradient-ascent and energy-based
techniques. The performance of this new method is tested experimentally, with a
range of complex, multi-resolution primal-dual grids generated for various
coastal and regional ocean modelling applications.
