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

TL;DR

This paper introduces a rotated characteristic decomposition method for high-order multi-dimensional reconstructions that significantly reduces computational cost while effectively controlling oscillations in hyperbolic conservation law schemes.

Contribution

The paper presents a novel rotated characteristic decomposition technique that requires only one decomposition per reconstruction, improving efficiency in multi-dimensional high-order schemes.

Findings

Reduces computational cost of characteristic decomposition in multi-dimensional schemes

Effectively controls spurious oscillations in high-order reconstructions

Demonstrated efficiency with third-order WENO-FV scheme for Euler equations

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.