The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system

Abstract

In this paper, we propose the stabilized penalty-projection finite element method for solving the Navier-Stokes-Cahn-Hilliard-Oono system, which is used to simulate the movement of thrombus in the blood vessels. The proposed algorithms are based on mixed finite element method in spatial direction, combined with a backward-Euler scheme and penalty-projection scheme for temporal discretization. It is worth noting that the idea of introducing a stabilized term admits the energy laws of two fully discrete schemes. Moreover, the convergence error estimates for both the semi-discrete scheme and fully discrete schemes are established for the first time. Numerical experiments are also provided to verify our proposed methods, and to show the results of our schemes have good performance with the theoretical ones. Finally, the proposed schemes are successfully applied to study the movement status of thrombus in healthy and blocked arteries, respectively.