Paving the (right) way for DNS and LES on unstructured grids: (fully) conservative collocated/staggered discretizations

The essence of turbulence are the smallest scales of motion. They result from a subtle balance between convective transport and diffusive dissipation. Mathematically, these terms are governed by two differential operators differing in symmetry: the convective operator is skew-symmetric whereas the diffusive is symmetric and positive-definite. On the other hand, accuracy and stability need to be reconciled for simulations of turbulent flows in complex geometries. With this in mind, a fully-conservative discretization method for general unstructured grids was proposed in Ref. [1]: it exactly preserves the symmetries of the underlying differential operators on collocated grids. Hence, unlike other formulations, the discrete convective operator transports energy from a resolved scale of motion to other resolved scales without dissipating energy, as it should do from a physical point-of-view. Therefore, we think that apart from being a right approach for large-scale DNSs of turbulence, it also forms a solid basis for testing subgrid scale LES models. In this work, we will explore the possibility to build up staggered formulations based on the set of discrete operators defined for collocated meshes.F.X.T. and A.O. are financially supported by the Ministerio de Economía y Competitividad, Spain (ENE2017-88697-R). F.X.T. was supported by a Ramón y Cajal contract (RYC-2012-11996). Simulations were carried out on the MareNostrum 4 supercomputer at the BSC. The authors thankfully acknowledge these institutions.Peer ReviewedPostprint (published version