Modern high order numerical Methods based on No-compromise moving Voronoi Tessellations: a Unified solver for continuum Mechanics

MoMeNTUM aims at developing a next-generation computational code for Hyperbolic balance laws influid flow and solid mechanics, based on versatile unstructured Voronoi grids (polygons andpolyhedra), and achieving efficiency that can be compared even with that of structured Cartesiancodes.

The space-time-based methods will be of high-order Arbitrary-Lagrangian-EulerianDiscontinuous Galerkin Finite Element type, with Finite Volume auxiliary subcell stabilisation.

Sucha mixed formulation requires new grid generation techniques in order to be extended to movingVoronoi meshes, due to the presence of degenerate and almost-degenerate elements with short orzero-length edges.

Using genuine Voronoi tessellations (i.e. nearest neighbour) is important inorder to preserve the smooth dynamic connectivity rearrangement naturally emerging from the motionof Voronoi seeds in space, which is a key element for the construction of robust schemes on movingpolyhedral grids.Efficiency will be achieved through new hybrid nodal/modal moving basis functions, defined oncell-aligned bounding boxes, that can heavily exploit tensor-type data storage and accesspatterns, usually available only in structured codes.Additionally, the schemes will be equipped with an embedded mesh generator that can synergisticallyinteract with the computational core so that the behaviour of the on-the-fly subgrid generator forthe Finite Volume subcells will be optimised, like the Voronoi grid motion, according to the localflow or stress patterns.The project is a heavily multidisciplinary effort that requires the development and implementationof new numerical solvers and new mesh generation algorithms within a single coherent softwarearchitecture, which will be packaged in an open source, massively parallel, high performance Fortrancode, in the hope that it will constitute a step forward towards the wide adoption of advancedhigh-order methods for solving real-world continuum mechanics problems.