A novel efficient reconstruction scheme for unstructured grids based on iterative least-squares methods

Yoshiharu Tamaki, Taro Imamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

A new compact higher-order variable reconstruction scheme based on iterative least-squares methods is proposed. The approximation of derivatives is split into multi-step first-order least-squares methods, and then converges to higher-order values through iteration. The scheme is defined only by the values stored in the face-adjacent cells. The size of the stencils and reconstruction matrix, and thus the computational cost and memory consumption is significantly reduced. In a time-evolutional problem, the converged value at the previous time-step is used as an initial value of the iteration in order to achieve quick convergence. In addition, a WENO-like weight function is implemented for shock-capturing problems. In a vortex-advection problem, it is shown that only one iteration of the reconstruction per time-step gives sufficient convergence, and that higher-order accuracy is achieved efficiently. Then a double-Mach reflection problem is simulated. The present scheme shows high resolution of the unsteady flow structure, and no severe numerical instability is observed. The computational cost of the fourth-order iterative reconstruction is cheaper than the conventional k -exact reconstruction with the same order of accuracy.

Original languageEnglish
Title of host publication54th AIAA Aerospace Sciences Meeting
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624103933
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event54th AIAA Aerospace Sciences Meeting, 2016 - San Diego, United States
Duration: 2016 Jan 42016 Jan 8

Publication series

Name54th AIAA Aerospace Sciences Meeting
Volume0

Other

Other54th AIAA Aerospace Sciences Meeting, 2016
CountryUnited States
CitySan Diego
Period16/1/416/1/8

ASJC Scopus subject areas

  • Aerospace Engineering

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