A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem (Advances in Applied Mathematics and Mechanics, 2022)
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-centeredmethod, 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 andnonphysical oscillation. Block-centered method is conservative locally. An upwindmethod with block-centered difference is used for computing the concentration. Thesaturations of different components are solved by the method of upwind fractionalstep difference, and the computational work is shortened significantly by dividing athree-dimensional problem into three successive one-dimensional problems and usingthe method of speedup. Using the variation discussion, energy estimates, the methodof duality, and the theory of a priori estimates, we complete numerical analysis. Finally, numerical tests are given for showing the computational accuracy, efficiency andpracticability of our approach.