A New Troubled-Cell Indicator for Discontinuous Galerkin Methods Using K-Means Clustering

Zhu, Hongqiang; Wang, Haiyun; Gao, Zhen

doi:10.1137/20m1344081

Cited by 4 publications

(1 citation statement)

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“…The Weak Adversarial Network [40] is tailored for high-dimensional PDEs in their weak form. Another idea is to train specific models offline to augment traditional numerical methods, which includes integrating discontinuity or trouble-cell detectors into hybrid WENO schemes [41,42], enhancing shock capturing techniques on Cartesian or unstructed grid [43,44], and refining conventional limiters [45,46]. Tompson et al [47] proposed a data-driven method to expedite solving incompressible Euler equations, and Liu et al [48] developed an artificial neural network to fine-tune the non-linear weights in the WENO-JS scheme.…”

Section: Introductionmentioning

confidence: 99%

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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The crystallization kinetics and melting behavior of nylon 10,10 in neat nylon 10,10 and in nylon 10,10 -montmorillonite (MMT) nanocomposites were systematically investigated by differential scanning calorimetry. The crystallization kinetics results show that the addition of MMT facilitated the crystallization of nylon 10,10 as a heterophase nucleating agent; however, when the content of MMT was high, the physical hindrance of MMT layers to the motion of nylon 10,10 chains retarded the crystallization of nylon 10,10, which was also confirmed by polarized optical microscopy. However, both nylon 10,10 and nylon 10,10 -MMT nanocomposites exhibited multiple melting be-havior under isothermal and nonisothermal crystallization conditions. The temperature of the lower melting peak (peak I) was independent of MMT content and almost remained constant; however, the temperature of the highest melting peak (peak II) decreased with increasing MMT content due to the physical hindrance of MMT layers to the motion of nylon 10,10 chains.

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