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 - <p style="text-align: justify;">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.</p>