A Rotated Characteristic Decomposition Technique for High-Order Reconstructions in Multi-dimensions

Hua Shen, Matteo Parsani

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
JournalJournal of Scientific Computing
Volume88
Issue number3
DOIs
StatePublished - Aug 11 2021

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Software
  • Engineering(all)

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