A COMBINATION METHOD OF MIXED FINITE VOLUME ELEMENT AND UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL COMPRESSIBLE DISPLACEMENT PROBLEMS
Numerical simulation of oil-water seepage displacement is a fundamental problem of energy science, where the mathematical model is defined by a nonlinear system of partial differential equations. The pressure is determined by a parabolic equation and the concentration is governed by a convection-diffusion equation. The pressure and Darcy velocity control the physical process of the concentration. A mixed volume element, a conservative scheme, is presented for approximating the pressure and Darcy velocity. The procedures improve the accuracy of Darcy velocity by one order. A second-order upwind fractional step difference scheme is used to obtain the concentration, and numerical oscillation and dispersion could be avoided well. Computational work is reduced greatly by decomposing the whole computation into successive one-dimensional subcomputations, where speedup solvers are used. Applying numerical theory and techniques of partial differential equations, we derive an optimal second-order error estimate in L2-norm. An extended argument is illustrated for the actual numerical model of multicomponent compressible enhanced oil recovery problem. The theoretical values are well shown in this paper for solving such a well-known problem in numerical simulation of energy science.
three-dimensional compressible displacement of oil-water flow, mixed finite volume element, modified upwind fractional step difference, second-order estimate in L2-norm, multicomponent compressible flow.
Received: October 8, 2020; Accepted: November 10, 2020; Published: January 22, 2021
How to cite this article: Changfeng Li, Yirang Yuan, Tongjun Sun and Qing Yang, A combination method of mixed finite volume element and upwind fractional step difference for three-dimensional compressible displacement problems, Far East Journal of Applied Mathematics 109(1) (2021), 1-47. DOI: 10.17654/AM109010001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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