A parallel, non-spatial iterative, and rotational pressure projection method for the nonlinear fluid-fluid interaction

Abstract

In this paper, a parallel, non-spatial iterative, and rotational pressure projection method for the coupled Navier-Stokes equations is proposed and developed. As for each Navier-Stokes equation, one elliptic equation and one Possion equation at each time step determine the values of the velocity and pressure, respectively. Moreover, we only need to solve four simple linear equations, and the computational time of the whole system is greatly reduced. The rotational pressure projection method achieves the same accuracy as the traditional decoupled fractional time-stepping method. Furthermore, we apply the presented method, the rotational pressure projection method and the linear decoupled fractional time-stepping method to the submarine mountain problem. Compared to the streamline diagrams of these three methods from two aspects of accuracy and CPU times, we obtain that the presented method has good parallelism and is the most efficient method, the rotational pressure projection method is more efficient than the traditional decoupled fractional time-stepping method. Finally, numerical results verify that our proposed method has the high efficiency.