An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions
Year: 2020
Author: Li Chen, Ruo Li, Feng Yang
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 3 : pp. 491–517
Abstract
We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and applicable on flexible grids. We show that the finite volume schemes with the new reconstruction satisfy a local maximum principle with properly setup on time step length. Numerical examples are presented to show that the proposed scheme attains a third-order accuracy for smooth solutions in both 2D and 3D cases. It is indicated by numerical results that the local maximum principle is helpful to prevent overshoots in numerical solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0017
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 3 : pp. 491–517
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Quadratic reconstruction finite volume method local maximum principle scalar conservation law unstructured mesh.
Author Details
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