PICIN: A Particle-in-Cell Solver for Incompressible Free Surface Flows with Two-Way Fluid-Solid Coupling

Abstract

This paper details a novel numerical approach for solution of the Navier-Stokes equations for free surface flows involving two-way fluid-solid interaction in arbitrary domains. The approach, which is hybrid Eulerian Lagrangian in nature, is based on the full particle particle-in-cell (PIC) method applied to incompressible flows. An extension of the distributed Lagrange multiplier (DLM) technique proposed by Patankar et al. [Int. J. Multiphase Flow, 26 (2000), pp. 1509-1524] is employed for the two-way fluid-solid coupling. The resulting code is called PICIN. Solid bodies can be mobile, either having prescribed motion or moving as a consequence of interaction with the fluid. Numerical results for three distinct example applications of the model in two spatial dimensions are given. A comparison of PICIN predictions with state-of-the-art numerical results of other researchers is made for each of the test cases presented.

A high‐order PIC method for advection‐dominated flow with application to shallow water waves

“…Existing PIC methods use assignment (kernel) functions to transfer the particles values to the grid. 11,12 However, the majority of these functions only have first-order accuracy in space when the particles are not uniformly distributed. 13 Because of this, instead of using a traditional smoothed particle hydrodynamics-type kernel function, we consider a high-order interpolation from the particles to the grid.…”

“…One well-known problem of the PIC method is that the particle distribution in space tends to become progressively less uniform as time evolves. 12 This can lead to the formation of large gaps between particles and particle clumping (especially around shocks). In the context of the NLSW equation solver, developed in Section 5, this can cause inaccurate depth and momentum transfers.…”

A hybridized discontinuous Galerkin framework for high-order particle–mesh operator splitting of the incompressible Navier–Stokes equations

“…[3]). Moreover, in recent work the method has also been applied in an engineering context for simulating free-surface flows [4,5,6]. An extension of the FLIP method to history-dependent materials was made by Sulsky and coworkers [7].…”

“…cellwise or even pointwise) divergence-free in order to maintain a uniform particle distribution, while also an accurate particle advection scheme must be used. Other authors pursue a more heuristic particle distribution quality control by either introducing weak spring forces between particles [4,15,21], or by using particle reseeding [13] or particle splitting [16] techniques.…”

Three-Dimensional Numerical Method for Simulating Large-Scale Free Water Surface by Massive Parallel Computing on a GPU

“…Therefore, the free surface flows with obvious three-dimensional (3-D) features should be simulated by 3-D methods. Traditionally, 3-D numerical methods developed for free-surface flows are mainly based on gas-liquid two-phase flow models [6], interface tracking models (common approaches include Volume of fluid (VOF) [7], level set [8], phase field [9]), and interface capturing models (including moving mesh approach [10], marker and cell (MAC) method [11], and particle-in-cell approach [12]). However, simulating LS-FS flows, particularly those in the area of hydraulic projects, requires a remarkable amount of computing resources, while it is challenging to maintain the stability and accuracy of the simulation.The single phase free surface lattice Boltzmann (SPFS-LB) model was originally proposed by Thürey in 2003 [13].…”