A data-driven shock capturing approach for discontinuous Galekin methods

Yu, Jian; Hesthaven, Jan S.

doi:10.1016/j.compfluid.2022.105592

Cited by 11 publications

(2 citation statements)

References 61 publications

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“…Several researchers have proposed data-driven shock detection [19][20][21] or capturing methods [22,23]. However, all of them have in common that they were trained in a supervised learning (SL) manner, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…during the training, none of the models actually took the response of the numerical scheme on their prediction into account. Thus, in the approaches available, either known shock capturing schemes were replaced by a data-driven model [22,23], or models were trained to classify between a numerically sound and a troubled solution [19][20][21]. The latter ansatz is quite intricate as the user has to classify the training samples a priori.…”

Section: Introductionmentioning

confidence: 99%

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A Reinforcement Learning Based Slope Limiter for Second‐Order Finite Volume Schemes

Schwarz

Keim

Chiocchetti

et al. 2023

Proc Appl Math and Mech

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Hyperbolic equations admit discontinuities in the solution and thus adequate and physically sound numerical schemes are necessary for their discretization. Second‐order finite volume schemes are a popular choice for the discretization of hyperbolic problems due to their simplicity. Despite the numerous advantages of higher‐order schemes in smooth regions, they fail at strong discontinuities. Crucial for the accurate and stable simulation of flow problems with discontinuities is the adequate and reliable limiting of the reconstructed slopes. Numerous limiters have been developed to handle this task. However, they are too dissipative in smooth regions or require empirical parameters which are globally defined and test case specific. Therefore, this paper aims to develop a new slope limiter based on deep learning and reinforcement learning techniques. For this, the proposed limiter is based on several admissibility constraints: positivity of the solution and a relaxed discrete maximum principle. This approach enables a slope limiter which is independent of a manually specified global parameter while providing an optimal slope with respect to the defined admissibility constraints. The new limiter is applied to several well‐known shock tube problems, which illustrates its broad applicability and the potential of reinforcement learning in numerics.

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