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arXiv · 2506.19370

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance

Daniel V. Leibovici·Oscar P. Bruno
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Abstract

This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation of the scheme with high-quality weak and strong scalability properties, and it illustrates the overall methodology for a variety of tests for the 2D Euler equations--including supersonic and hypersonic flows and shocks past obstacles with corners. The results produces by the new methods are compared to previous theoretical and experimental results, and the high parallel scalability of the algorithm is demonstrated in both weak and strong scaling cases. Thanks to its use of a localized yet smooth artificial viscosity term--whose support is confined to regions near flow discontinuities identified by an artificial neural network--the algorithm maintains minimal numerical dissipation away from discontinuities. Overall, the method delivers accurate, sharp resolution of shocks and contact discontinuities, while producing smooth numerical solutions in regular flow regions--as evidences by the near-complete absence of spurious oscillations in level-set contours, even under strong shocks and high-speed flow conditions.

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Daniel V. Leibovici, Oscar P. Bruno. 2025-06-24. General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance. https://arxiv.org/abs/2506.19370

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