TY - JOUR
T1 - Positive and Conservative Characteristic Block-Centered Finite Difference Methods for Convection Dominated Diffusion Equations
AU - Li , Xinshu
AU - Fu , Kai
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1087
EP - 1110
PY - 2022
DA - 2022/06
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2021-0051
UR - https://global-sci.org/intro/article_detail/aamm/20553.html
KW - Positivity preserving, conservative, characteristic method.
AB - <p style="text-align: justify;">In this work, spatial second order positivity preserving characteristic block-centered finite difference methods are proposed for solving convection dominated diffusion problems. By using a conservative piecewise parabolic interpolation with positive constraint, the temporal first order scheme is shown to conserve mass exactly and
preserve the positivity property of solution. Taking advantage of characteristics, there
is no strict restriction on time steps. The scheme is extended to temporal second order by using a particular extrapolation along the characteristics. To restore solution
positivity, a mass conservative local limiter is introduced and verified to keep second
order accuracy. Numerical examples are carried out to demonstrate the performance
of proposed methods.</p>