The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system
The authors are concerned with the penalty-projection FEM as a solver for the Navier-Stokes-Cahn-Hilliard-Oono system in a bounded 2D domain modeling the phase-field of two-phase flows. They introduce a mixed finite element method to solve the penalized system instead of the original one and derive the optimal error estimates for finite element approximation in the case of piecewise linear basis functions. Then, they consider two stabilized fully discrete schemes for the original formulation, based on time discretization of the penalized finite element system. The backward-Euler scheme and the penalty-projection scheme are proposed for the temporal approximation. The convergence of both fully discrete schemes is proved. These discrete schemes remain stable and satisfy energy laws. Some numerical experiments are carried out in order to prove the validity and effectiveness of the proposed scheme, and to simulate the phenomena of thrombus motion in atherosclerosis flow.
scientific article; zbMATH DE number 7354396
scientific article