A Cartesian cut cell based two-way strong fluid–solid coupling algorithm for 2D floating bodies

Abstract

In a recent paper Kelly et al. (2015) [PICIN: A Particle-In-Cell solver for incompressible free surface flows with two-way fluid-solid coupling. SIAM Journal on Scientific Computing 37 (3), B403-B424.] detailed the PICIN full particle Particle-In-Cell (PIC) solver for incompressible free-surface flows. The model described in that paper employed a tailored version of the Distributed Lagrange Multiplier (DLM) method for the strong coupling of fluid-solid interaction. In this paper we propose an alternative strong fluid-solid coupling algorithm based on a modification to the cut cell methodology that is informed by the variational approach. The solid velocity flux/integral on the boundary is expressed purely in terms of pressure leading to a revised pressure Poisson equation that is discretised in a finite volume sense. This approach allows the PICIN model to simulate the motion of floating bodies of arbitrary configuration. 2D test cases involving floating bodies with one or more degrees of freedom (DoF) are used to validate the modified PICIN model. The results presented show that the modified PICIN model is able to both efficiently and robustly predict the motions of surface-piercing floating structures under either regular or extreme wave action.

A combined level set/ghost cell immersed boundary representation for floating body simulations

“…A curvilinear immersed boundary method was used for the fluid‐solid interface . Chen et al presented a strong, two‐way, fluid‐solid coupling algorithm, based on a variational‐type cut cell methodology, implemented within a hybrid Eulerian–Lagrangian framework.…”

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

“…the method proposed by Glowinski [25]). Similarly to the latter approach, we split the governing equations (1)(2)(3)(4)(5)(6) into an advection problem and an incompressible Stokes problem. For illustrative purposes we present a particular splitting procedure below, containing the essential components.…”

“…However, we strictly avoid the heuristic damping term in the mesh-particle projection which is often used in the aforementioned methods to enhance stability for advection-dominated problems (see e.g. [5,9,13]).…”

“…[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].…”

SPH Simulation of Wave Scattering by a Heaving Submerged Horizontal Plate

“…Moreover, the heave amplitude of the plate is comparatively large when the elastic support is weak. Severe distortion may happen on the¯tted-body moving grid, or within the¯xed grid regime, the immersed boundary method (Peng et al [2013]) or the cut-cell approach (Chen et al [2016]) needs to be introduced to handle the°uid-solid interface.…”