| Abstract: |
| This work is concerned with mathematical modeling and numerical simulations of the steady state and the movements of} complex fluids involved in oil exploitation practice. Capillary pressure caused by surface tension at the interface between every two adjacent different phases of the mixture is viewed as the leading force in oil recovery from fractured oil reservoirs. Therefore, the interface between contiguous phases has become a critical mathematical modeling aspect. The diffuse interface theory is our institutive choice. The density of the homogeneous part and the parameters of the gradient part of the Helmholtz free energy are provided by the widely used Peng-Robinson equation of state (EOS). The fourth-order parabolic equation is derived and solved numerically by several energy stable schemes to describe the evolution processes of one-component, two-phase substances. The theoretical analyses of these numerical schemes have been obtained to demonstrate their mass conservation, energy stability, unique solvability and convergence. |
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