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 in

fluid flow and solid mechanics, based on versatile unstructured Voronoi grids (polygons and

polyhedra), and achieving efficiency that can be compared even with that of structured Cartesian

codes. The space-time-based methods will be of high-order Arbitrary-Lagrangian-Eulerian

Discontinuous Galerkin Finite Element type, with Finite Volume auxiliary subcell stabilisation. Such

a mixed formulation requires new grid generation techniques in order to be extended to moving

Voronoi meshes, due to the presence of degenerate and almost-degenerate elements with short or

zero-length edges. Using genuine Voronoi tessellations (i.e. nearest neighbour) is important in

order to preserve the smooth dynamic connectivity rearrangement naturally emerging from the motion

of Voronoi seeds in space, which is a key element for the construction of robust schemes on moving

polyhedral grids.

Efficiency will be achieved through new hybrid nodal/modal moving basis functions, defined on

cell-aligned bounding boxes, that can heavily exploit tensor-type data storage and access

patterns, usually available only in structured codes.

Additionally, the schemes will be equipped with an embedded mesh generator that can synergistically

interact with the computational core so that the behaviour of the on-the-fly subgrid generator for

the Finite Volume subcells will be optimised, like the Voronoi grid motion, according to the local

flow or stress patterns.

The project is a heavily multidisciplinary effort that requires the development and implementation

of new numerical solvers and new mesh generation algorithms within a single coherent software

architecture, which will be packaged in an open source, massively parallel, high performance Fortran

code, in the hope that it will constitute a step forward towards the wide adoption of advanced

high-order methods for solving real-world continuum mechanics problems.