Robust and reliable DNS and LES on unstructured grids

Preserving the operators symmetries at discrete level is the key aspect to enable reliable DNS and LES simulations of turbulent flows. On the other hand, realworld applications demand robust and stable numerical methods suitable for complex geometries. In this regard, this work presents a symmetry-preserving discretization for unstructured collocated grids that, apart from being virtually free of artificial dissipation, it is shown to be unconditionally stable. Special attention is given to the (de)construction of the discrete operators into fundamental geometrical entities. On this basis, a new inexpensive method to compute strict eigenbounds for the convective and diffusive operators, which are needed to determine the time-step à la CFL, is presented. Apart from providing better estimations than previous methods, it is relies on a sparsematrix vector product where only vectors change on time. Hence, both implementation in existing codes and cross-platform portability are straightforward. Altogether leads to a simple and robust approach for DNS and LES simulations of complex turbulent flows.
F.X.T., J.A.H,D. Sand A.O. are supported by the Ministerio de Economía y Competitividad, Spain, RETO twin project (PDC2021-120970-I00). Calculations were carried out on MareNostrum4 supercomputer at BSC.We thankfully acknowledge these institutions.
Postprint (published version)