Volume 14, Issue 6
A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem

Adv. Appl. Math. Mech., 14 (2022), pp. 1246-1275.

Published online: 2022-08

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• Abstract

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.

• AMS Subject Headings

65N12, 65N30, 65M12, 65M15

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@Article{AAMM-14-1246, author = {Li , ChangfengYuan , YirangCheng , Aijie and Song , Huailing}, title = {A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {6}, pages = {1246--1275}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0284}, url = {http://global-sci.org/intro/article_detail/aamm/20847.html} }
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 -

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.

Changfeng Li, Yirang Yuan, Aijie Cheng & Huailing Song. (2022). A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem. Advances in Applied Mathematics and Mechanics. 14 (6). 1246-1275. doi:10.4208/aamm.OA-2021-0284
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