A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions
A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions
复制标题
多维高阶重构的旋转特征分解技术
DOI：
10.1007/s10915-021-01602-z
复制
发表时间：
2021
影响因子：
2.5
通讯作者：
Matteo Parsani
中科院分区：
文献类型：
--
作者：
Hua Shen;Matteo Parsani
在构造求解双曲型守恒律方程的高阶格式时，通常在特征空间中进行相应的高阶重构，以尽可能地消除伪振荡。对于多维有限体积（FV）格式，我们需要在目标单元的不同法线方向上多次进行特征分解，这是非常耗时的。在本文中，我们提出了一种旋转的特征分解技术，只需要一次分解的多维重建。旋转方向仅取决于特定物理量的梯度，这是廉价的计算。该技术不仅显著降低了计算量，而且有效地抑制了寄生振荡。以求解Euler方程的三阶加权基本无振荡有限体积（WENO-FV）格式为例，验证了该方法的有效性.
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.