TY - JOUR
T1 - An Upwind Multistep Difference with Mixed Finite Volume Element Method for a Positive Semi-Definite Contamination Treatment Problem
AU - Li , Changfeng
AU - Yuan , Yirang
AU - Song , Huailing
JO - Analysis in Theory and Applications
VL - 2
SP - 111
EP - 139
PY - 2025
DA - 2025/07
SN - 41
DO - http://doi.org/10.4208/ata.OA-2022-0024
UR - https://global-sci.org/intro/article_detail/ata/24279.html
KW - Positive semi-definite problem, upwind multistep difference with mixed finite volume element, local conservation, convergence analysis, numerical experiments.
AB - <p style="text-align: justify;">A positive semi-definite problem of three-dimensional incompressible contamination treatment from nuclear waste in porous media is discussed in this paper.
The mathematical model is defined by a nonlinear initial-boundary system consisting
of partial differential equations. Four important equations (an elliptic equation, two
convection-diffusion equations and a heat conductor equation) determine the physical
features. Considering the physical natures and computational efficiency, the authors
introduce the conservative mixed finite volume element, upwind approximation and
multistep difference to solve this system. The pressure and Darcy velocity are computed by a mixed finite volume element. The concentrations and temperature are
solved by a combination of upwind approximation, multistep difference and mixed
finite volume element. A multistep difference is used for approximating the partial
derivative with respect to time. Mixed finite volume element and upwind differences
are given for solving the convection-diffusions equations. Numerical dispersion and
nonphysical oscillations could be eliminated, and the computational efficiency is improved by using a large time step. Furthermore, a conservative law is preserved and
error estimates in $L^2$-norm is obtained. Finally, two numerical experiments are given
to show the efficiency and possible applications.</p>