Third order maximumprinciplesatisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes
We develop 3rd order maximumprinciplesatisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β _{0},β _{1}) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximumprinciplesatisfying limiter.
 Authors:

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 Iowa State Univ., Ames, IA (United States)
 Zhejiang Ocean Univ., Zhejiang (China); Key Lab. of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhejiang (China)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 308; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; discontinuous Galerkin methods; convection diffusion equation; maximum principle; positivity preserving; incompressible Navier–Stokes equations
 OSTI Identifier:
 1330548
Chen, Zheng, Huang, Hongying, and Yan, Jue. Third order maximumprinciplesatisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes. United States: N. p.,
Web. doi:10.1016/j.jcp.2015.12.039.
Chen, Zheng, Huang, Hongying, & Yan, Jue. Third order maximumprinciplesatisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes. United States. doi:10.1016/j.jcp.2015.12.039.
Chen, Zheng, Huang, Hongying, and Yan, Jue. 2015.
"Third order maximumprinciplesatisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes". United States.
doi:10.1016/j.jcp.2015.12.039. https://www.osti.gov/servlets/purl/1330548.
@article{osti_1330548,
title = {Third order maximumprinciplesatisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes},
author = {Chen, Zheng and Huang, Hongying and Yan, Jue},
abstractNote = {We develop 3rd order maximumprinciplesatisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β0,β1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximumprinciplesatisfying limiter.},
doi = {10.1016/j.jcp.2015.12.039},
journal = {Journal of Computational Physics},
number = C,
volume = 308,
place = {United States},
year = {2015},
month = {12}
}