Computational Mathematics and Scientific Computing Seminar

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A method for solving multi-species and shock-laden flow at unprecedented problem sizes and time-to-solution is presented. Based on recent work of F. Schäfer and the speaker, an 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., GH200, MI300A), typically used on current 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, memory footprint, and energy-to-solution metrics. The reduced memory footprint compared to baselines enables 25-times larger simulations, exceeding 200T grid points (1 quadrillion degrees of freedom) 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 200B grid point flow simulation in less than one wall time minute on OLCF Frontier.