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arXiv · 1703.01055

Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids

Li Chen·Guanghui Hu·Ruo Li
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Abstract

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.

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Li Chen, Guanghui Hu, Ruo Li. 2018-04-21. Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids. https://doi.org/10.4208/cicp.oa-2017-0137

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