Coupling finite difference method with finite particle method for modeling viscous incompressible flows

Abstract

Summary A hybrid approach to couple finite difference method (FDM) with finite particle method (FPM) (ie, FDM‐FPM) is developed to simulate viscous incompressible flows. FDM is a grid‐based method that is convenient for implementing multiple or adaptive resolutions and is computationally efficient. FPM is an improved smoothed particle hydrodynamics (SPH), which is widely used in modeling fluid flows with free surfaces and complex boundaries. The proposed FDM‐FPM leverages their advantages and is appealing in modeling viscous incompressible flows to balance accuracy and efficiency. In order to exchange the interface information between FDM and FPM for achieving consistency, stability, and convergence, a transition region is created in the particle region to maintain the stability of the interface between two methods. The mass flux algorithm is defined to control the particle creation and deletion. The mass is updated by N‐S equations instead of the interpolation. In order to allow information exchange, an overlapping zone is defined near the interface. The information of overlapping zone is obtained by an FPM‐type interpolation. Taylor‐Green vortices and lid‐driven shear cavity flows are simulated to test the accuracy and the conservation of the FDM‐FPM hybrid approach. The standing waves and flows around NACA airfoils are further simulated to test the ability to deal with free surfaces and complex boundaries. The results show that FDM‐FPM retains not only the high efficiency of FDM with multiple resolutions but also the ability of FPM in modeling free surfaces and complex boundaries.

A Review of SPH Techniques for Hydrodynamic Simulations of Ocean Energy Devices

“…This work was further improved by Chiron et al [257] in 2018 by allowing net mass transferring between the SPH and FV domain and free-surface crossing the overlapping domain, which makes the coupling scheme more suitable for simulating wave-structure-interaction problems. Note that in addition to FV, SPH-FD coupling is also a feasible strategy (see, e.g., [258,259]). In the OEDs scenario, the coupled SPH-FV framework is very suitable for the wavestructure interactions because such a type of simulations is usually characterized by a huge computational domain and violent free-surface evolutions in the vicinity of OEDs.…”

Lagrangian radial basis function‐based particle hydrodynamics method and its application for viscous flows

“…For time integral scheme, the predictor–corrector time integration algorithm 59 is adopted. During the first half of the time step, is predicted using the following scheme: …”

“…Similarly, the predictor–corrector time integration algorithm is adopted as the time integral scheme 59 . The principle of selecting time step is Δ t < CFL × h /( c + u top ) and CFL = 0.2 in this study.…”

“…According to the particle position, the particles are divided into fluid particles, boundary particles, and virtual particles. The periodical boundary condition 59 is implemented on the square boundaries. For example, the field variables of boundary and virtual particles located on left boundary are equal to those of fluid particles near the right boundary.…”

“…The artificial viscous term is added inside the momentum equation for incompressible fluids 74 . To satisfy the dynamics boundary of free surface, 75 the dynamic viscous coefficient μ in Equation (38) is theoretically given in two dimension 59 by: where the artificial viscous coefficient α is chosen in the range [0.01, 0.05] 71 …”