TY - JOUR T1 - An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions AU - Chen , Li AU - Li , Ruo AU - Yang , Feng 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.