Volume 1, Issue 3
An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions

Li Chen, Ruo Li & Feng Yang

CSIAM Trans. Appl. Math., 1 (2020), pp. 491-517.

Published online: 2020-09

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  • 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.

  • Keywords

Quadratic reconstruction, finite volume method, local maximum principle, scalar conservation law, unstructured mesh.

  • AMS Subject Headings

65M08, 76M12, 90C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-491, author = {Li Chen , and Ruo Li , and Feng Yang , }, title = {An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {3}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0017}, url = {http://global-sci.org/intro/article_detail/csiam-am/18305.html} }
TY - JOUR T1 - An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions AU - Li Chen , AU - Ruo Li , AU - Feng Yang , JO - CSIAM Transactions on Applied Mathematics VL - 3 SP - 491 EP - 517 PY - 2020 DA - 2020/09 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0017 UR - https://global-sci.org/intro/article_detail/csiam-am/18305.html KW - Quadratic reconstruction, finite volume method, local maximum principle, scalar conservation law, unstructured mesh. AB -

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.

Li Chen, Ruo Li & Feng Yang. (2020). An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions. CSIAM Transactions on Applied Mathematics. 1 (3). 491-517. doi:10.4208/csiam-am.2020-0017
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