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A Rotated Characteristic Decomposition Technique for High-Order Reconstructions in Multi-dimensions

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Abstract

When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume (FV) schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. In this paper, we propose a rotated characteristic decomposition technique which requires only one-time decomposition for multi-dimensional reconstructions. The rotated direction depends only on the gradient of a specific physical quantity which is cheap to calculate. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume (WENO-FV) scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique.

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Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

H.S. acknowledges the financial support of National Natural Science Foundation of China (Contract No. 11901602).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China

    Hua Shen

  2. Extreme Computing Research Center (ECRC), Computer, Electrical and Mathematical Sciences and Engineering (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia

    Matteo Parsani

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  1. Hua Shen
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  2. Matteo Parsani
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Correspondence to Hua Shen.

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This work was supported by the National Natural Science Foundation of China (Contract No. 11901602).

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Shen, H., Parsani, M. A Rotated Characteristic Decomposition Technique for High-Order Reconstructions in Multi-dimensions. J Sci Comput 88, 87 (2021). https://doi.org/10.1007/s10915-021-01602-z

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