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.

在构造求解双曲守恒定律的高阶方案时，通常在特征空间中进行相应的高阶重构，以尽可能消除伪振荡。对于多维有限体积（FV）方案，我们需要在目标单元的不同法线方向上进行多次特征分解，非常耗时。在本文中，我们提出了一种旋转特征分解技术，该技术只需要一次分解即可进行多维重建。旋转方向仅取决于计算成本低的特定物理量的梯度。该技术不仅显着降低了计算成本，而且有效地控制了虚假振荡。