Parallelization of compact finite-volume schemes for turbulent compressible flow

Compact schemes are widely employed in numerical simulations of turbulent flows, because of their beneficial resolution properties and high overall accuracy. However, the implicit nature of such methods makes them difficult to use in a parallel framework, especially when a MPI-based multi-block partitioning technique is adopted. Previous attempts fall mainly into two categories: 1. use of parallel algorithms for solving the linear system of equations over the entire domain; 2. use of explicit or asymmetric stencils at block-to-block connections to obtain disjoint matrix systems. While the first approach can suffer from low parallel efficiency, the second one has received considerable attention over the last years and is now an active field of research. The main advantage of this procedure is to lead to disjoint matrix systems that can be solved independently by exchanging a (small) number of halo cells between the blocks. Unfortunately, breaking the global dependance results in altered dissipation and dispersion properties, which are well-known to be crucial in LES and DNS of turbulent flows. The aim of the present study is to construct a robust parallelization strategy for finite-volume compact schemes on multi-block domains. Particular attention is paid to spectral properties, conservativeness and accuracy of the resulting methods.