TY - JOUR
T1 - A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem
AU - Li , Changfeng
AU - Yuan , Yirang
AU - Cheng , Aijie
AU - Song , Huailing
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1246
EP - 1275
PY - 2022
DA - 2022/08
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2021-0284
UR - https://global-sci.org/intro/article_detail/aamm/20847.html
KW - Chemical oil recovery, upwind block-centered difference, fractional step difference, elemental conservation, convergence analysis.
AB - <p style="text-align: justify;">A kind of conservative upwind method is discussed for chemical oil recovery displacement in porous media. The mathematical model is formulated by a nonlinear convection-diffusion system dependent on the pressure, Darcy velocity, concentration and saturations. The flow equation is solved by a conservative block-centered
method, and the pressure and Darcy velocity are obtained at the same time. The concentration and saturations are determined by convection-dominated diffusion equations, so an upwind approximation is adopted to eliminate numerical dispersion and
nonphysical oscillation. Block-centered method is conservative locally. An upwind
method with block-centered difference is used for computing the concentration. The
saturations of different components are solved by the method of upwind fractional
step difference, and the computational work is shortened significantly by dividing a
three-dimensional problem into three successive one-dimensional problems and using
the method of speedup. Using the variation discussion, energy estimates, the method
of duality, and the theory of a priori estimates, we complete numerical analysis. Finally, numerical tests are given for showing the computational accuracy, efficiency and
practicability of our approach.</p>