Enhanced Data-Driven HLLC Riemann Solver
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This work addresses the accuracy and stability limitations of approximate Riemann solvers, such as the Harten-Lax-van Leer-Contact (HLLC) [1] solver, in challenging flow conditions like strong rarefactions. To overcome these issues, we explore two data-driven frameworks using deep neural networks (NNs) [2]. The first is a pure NN solver trained to predict the exact Riemann solution, which achieves high accuracy but at a significant computational cost. The second, and more efficient proposal is a hybrid scheme. This method uses the standard HLLC solver as its baseline but augments it with a simple physics-based detector that identifies interfaces where HLLC is likely to fail. At only these problematic interfaces, the scheme switches to the pre-trained NN solver. Benchmark tests demonstrate that this hybrid approach achieves an accuracy level comparable to the pure NN solver while maintaining a computational cost nearly identical to the standard HLLC solver, thus offering a superior balance of efficiency and robustness.