@Article{CiCP-24-454,
author = {Li Chen, Guanghui Hu and Ruo Li},
title = {Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {2},
pages = {454--480},
abstract = {<p style="text-align: justify;">In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172–1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to enforce a
local maximum principle is too restrictive to be satisfied by, for example, locally refined
meshes or distorted meshes generated by arbitrary Lagrangian-Eulerian methods in
practical applications. In this paper, we propose an improved integrated linear reconstruction approach to get rid of the geometric hypothesis. The resulting optimization
problem is a convex quadratic programming problem, and hence can be solved efficiently by classical active-set methods. The features of the improved integrated linear
reconstruction include that i). the local maximum principle is fulfilled on arbitrary unstructured grids, ii). the reconstruction is parameter-free, and iii). the finite volume
scheme is positivity-preserving when the reconstruction is generalized to the Euler
equations. A variety of numerical experiments are presented to demonstrate the performance of this method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0137},
url = {http://global-sci.org/intro/article_detail/cicp/12248.html}
}