Towards adaptive high-order simulations of multiphase compressible turbulent flows at exa-scale

Numerical simulations of turbulent flows require numerical methods which preserve the broadband multiscale dynamics of turbulence. Compressible and multiphase turbulent flows pose additional challenges including accurate treatment of acoustic waves, shock waves and its interaction with turbulence, and phase interface phenomena such as droplet breakup, atomization, cavitation, evaporation and condensation. Thermodynamics of the continuous phases also need to be appropriately and consistently treated. A high-accuracy solver capable of representing these physical complexities with minimum numerical dispersion and dissipation and designed for portability and performance scaling on exa-scale computing hardware would enable computational exploration of multi-physics turbulent flows at fundamental level and advance modeling approaches for applications ranging from sustainable energy to aerospace. Recent progress towards exa-scale capable compressible multiphase turbulent flow simulations is reviewed with emphasis on work at Stanford. Under support from NSF an open-source software framework called AMR-H is being developed. It combines robust high-accuracy compact-scheme based approach on curvilinear grids with shock capturing where required. For performance on HPC systems it combines Kokkos and Legion to support AMR for performance portability and runtime parallelism control. The banded linear systems arising with compact schemes (differentiation and interpolation) are efficiently solved using cyclic reduction considering both shared and distributed memory hierarchies. The scaling performance and turbulence physics results obtained on Summit at ORNL are discussed. Results on compressible isotropic turbulence, compressible shear layers, and supercritical wall-bounded turbulence are discussed, and the status of AMR software is summarized. Collaborations from the scientific community are sought to further advance the capabilities of this software infrastructure.