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arXiv · 2105.10106

A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions

Hua Shen·Matteo Parsani
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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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Hua Shen, Matteo Parsani. 2021-05-21. A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions. https://doi.org/10.1007/s10915-021-01602-z

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