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.

翻译：在设计解决双曲保护法的高序计划时,相应的高序重建通常在尽可能消除虚假振荡的特质空间进行。对于多维有限体积(FV)计划,我们需要在目标细胞的不同正常方向进行特性分解几次,这非常耗时。在本文中,我们建议一种旋转的特性分解技术,它只要求多维重建一次性分解。旋转的方向仅取决于特定物理量的梯度,而这种物质量是廉价的计算。这一技术不仅显著地降低了计算成本,而且还有效地控制了虚假振荡。我们用第三级的加权基本非振荡性体积(WENO-FV)计划来解决电动方程式,作为证明拟议技术效率的范例。