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A New Framework of Troubled-Cell Indicator on General Meshes for DG Methods Using Simple Statistical Analysis Techniques

A New Framework of Troubled-Cell Indicator on General Meshes for DG Methods Using Simple Statistical Analysis Techniques

Year:    2025

Author:    Hongqiang Zhu, Haiyun Wang, Zhihuan Wang, Rumeng Shao, Zhen Gao

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 392–414

Abstract

An accurate, efficient and robust troubled-cell indicator (TCI) is always required by the discontinuous Galerkin methods for solving the nonlinear system of hyperbolic conservation laws. In this paper, we propose a new framework of TCI on general meshes using simple statistical analysis techniques which is easy to implement and efficient to run. In the framework troubled-cell indication is performed in each local stencil. We first pick the local stencils that contain the troubled cells via the range of the normalized troubled-cell indication values, and then detect the troubled cells in each picked stencil by a simple separation approach. The new TCI framework is implemented on several types of meshes with three indication variables. Numerical experiments conducted through simulating several classical shocked flows demonstrate that the new framework can capture the locations of shock waves accurately and lead to essentially nonoscillatory solutions. The results also verify the robustness of the framework.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2023-317.170324

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 392–414

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Troubled-cell indicator limiter discontinuous Galerkin method statistical analysis.

Author Details

Hongqiang Zhu

Haiyun Wang

Zhihuan Wang

Rumeng Shao

Zhen Gao