An upwind-mixed volume element method on changing meshes for compressible miscible displacement problem

• Published in: Journal of computational and applied mathematics Vol. 446; p. 115829
• Main Authors: Yirang, Yuan, Changfeng, Li, Huailing, Song
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.08.2024
• Subjects: Convergence analysis; Local conservation of mass; MFVE-UMFVE on changing meshes; Numerical example; Three-dimensional compressible displacement; 65M15; 65N12; Three-dimensional compressible displacement; MFVE-UMFVE on changing meshes; 65M60; Local conservation of mass; 65N30; Convergence analysis; Numerical example
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2024.115829

Numerical simulation of oil-water miscible displacement is discussed in this paper, and a compressible problem of energy mathematics is solved potentially. The mathematical model defined by a nonlinear system includes mainly two partial differential equations (PDEs): a parabolic equation for the pressure and a convection-diffusion equation for the saturation. The pressure is obtained by a conservative mixed finite volume element method (MFVE). The computational accuracy is improved for Darcy velocity. A conservative upwind mixed finite volume element method (UMFVE) is applied to compute the saturation on changing meshes. The diffusion is discretized by a mixed finite volume element method, and the convection is computed by upwind differences. The upwind method can solve convection-dominated diffusion equations accurately and avoids numerical dispersion and nonphysical oscillation. The saturation and the adjoint vector function are obtained simultaneously. An optimal order error estimates is obtained. Finally, numerical examples are provided to show the accuracy, efficiency and possible applications.