Shocks without tracking or capturing: Exceeding 1 quadrillion degrees of freedom via inviscid regularization of the compressible Navier-Stokes

A method for solving multi-species and shock-laden flow at unprecedented problem sizes and time-to-solution is presented. The first inviscid regularization of the Navier-Stokes-like PDE is performed. This enables linear and well-conditioned numerics suitable for mixed-precision computation. A unified memory implementation is crafted for tightly coupled CPU-GPU and APU architectures (e.g., MI250X, GH200, MI300A), now standard on flagship machines like El Capitan and Frontier. With this trio, we improve on state-of-the-art CFD techniques with order of magnitude improvements along computational cost and memory footprint axes. The reduced memory footprint compared to baselines enables, for example, 25-times larger simulations, here shown to exceed 1 quadrillion degrees of freedom (200T grid points) with per-grid-point cost speedups. The method strong scales from 8 nodes to the full systems (>10K nodes) with better than 50% efficiency. This enables, for example, a typical 200B grid point CFD simulation in less than one wall clock minute on OLCF Frontier. Early results suggest increased robustness compared to ENO/limiter-type shock capturing schemes for high-Mach flows and strong discontinuities. Results are shown for a Mach 14 many-rocket-engine configuration that nominally matches the SpaceX Super Heavy.