Abstract 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.
The use of weighted primal-dual pairs has also been pursued by @cite_3 @cite_17 @cite_16 in which a multi-paradigm optimisation scheme is used to improve the well-centredness of two- and three-dimensional unstructured grids for co-volume type aerospace modelling. In this work, a novel modified cuckoo' type optimisation strategy is employed to minimise a dual mesh quality metric that measures the offset between dual vertices and their associated primal element centroids. These operations are combined with topological modifications, in which clusters of primal elements associated with sufficiently small dual edges are merged into polyhedra. report good performance for a variety of two- and three-dimensional problems, and demonstrate that optimised primal-dual meshes often improve the stability and efficiency of co-volume type solvers for problems in aerodynamics and electromagnetism.
@cite_16 @cite_3 @cite_17
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This paper discusses some engineering applications of gradient free optimisation techniques. This is achieved using the development of the cuckoo search algorithm as a case study. The motivations behind using gradient free algorithms are discussed and illustrated using two specific practical examples. The first involves aerofoil shape optimisation, where it is shown that a modified cuckoo search algorithm performs well when applied both to aerofoil inverse design and aerofoil shape optimisation. This example is then used to discuss the use of reduced order modeling to decrease the computational cost of the optimisation process. We discuss which reduced order modeling techniques based on proper orthogonal decomposition are suitable for these optimisation applications. The second example is that of co-volume mesh optimisation, where it is shown that a modified cuckoo search can significantly outperform alternative non-optimisation and gradient based techniques. We conclude by discussing a number of remaining difficulties which may deter engineers from using gradient free techniques, and suggest ways in which these may be alleviated. Abstract This paper introduces developments in modified techniques for the generation of unstructured, non-uniform, dual orthogonal meshes which are suitable for use with co-volume solution schemes. Two new mesh generation techniques, a modified advancing front technique and an octree-Delaunay algorithm, are coupled with a mesh optimisation algorithm. When using a Delaunay–Voronoi dual, to construct mutually orthogonal meshes for co-volume schemes, it is essential to minimise the number of Delaunay elements which do not contain their Voronoi vertex. These new techniques provide an improvement over previous approaches, as they produce meshes in which the number of elements that do not contain their Voronoi vertex is reduced. In particular, it is found that the optimisation algorithm, which could be applied to any mesh cosmetics problem, is very effective, regardless of the quality of the initial mesh. This is illustrated by applying the proposed approach to a number of complex industrial aerospace geometries. SUMMARY A new mesh optimisation scheme, reduced order mesh optimisation, is introduced. The technique uses proper orthogonal decomposition to reduce the number of dimensions in a mesh optimisation problem. This reduction in dimensionality allows the expression of the optimisation problem globally rather than the more traditional local mesh optimisation or smoothing algorithms. To perform the optimisation, the recently developed gradient-free technique modified cuckoo search is applied. The effectiveness of the algorithm is shown by considering the problem of optimising meshes for use in co-volume techniques. Co-volume techniques require the existence of two mutually orthogonal meshes; this is achieved by utilising the Delaunay–Voronoi dual. A combination of considering the problem globally and the use of a gradient-free technique results in a scheme that significantly outperforms previous methods in solving this particular problem. Although the examples presented in this paper are specific to optimising dual meshes, the technique is general and can be simply modified to any mesh optimisation problem. Copyright © 2012 John Wiley & Sons, Ltd.