Parallel embedded boundary methods for fluid and rigid-body interaction

Abstract

The implementations of an updated body-fitted and a non body-fitted method to deal with the interaction of a fluid and a rigid body are described. The physics of the fluid is modeled by the incompressible Navier-Stokes equations. A parallel fluid solver based on the VMS (Variational Multiscale) Finite Element method serves as the basis for the implementation. For the rigid body movement, the Newton-Euler equations are solved numerically. To account for the interaction, the force that the fluid exerts on the rigid body is determined, on the one hand. On the other hand, the velocity of the rigid body is imposed as a Dirichlet boundary condition on the fluid. A fixed Eulerian mesh discretizes the fluid domain, except for nodes in the vicinity of the rigid body boundary for the case of the updated body-fitted approach. The wet boundary of the rigid body is embedded in the fluid mesh and tracked by a moving surface mesh. It is a distinctive characteristic of the updated body-fitted strategy that, in order to impose velocities on the interface, some\ud of the nodes near the body surface are moved by using a local r-adaptivity algorithm to conform with this surface. By contrast, the non body-fitted approach uses kriging interpolation for velocity prescription over the fluid on the interface. Given that fluid nodes can become solid nodes and viceversa due to the rigid body movement, we have adopted the FMALE approach, a variation of the ALE method to keep the fluid mesh fixed. Algorithms to ensure high performance, like skd-trees to determine if a given spatial point is currently inside the solid, are also used. All these ingredients constitute two approaches that are both computationally efficient and accurate. Numerical experiments are presented to assess their performance comparatively.We would like to especially thank Oscar Peredo for his idea and support in introducing a more technical notation and terminology for the data-structures described in this work.Peer ReviewedPostprint (author's final draft

The use of artificial compressibility to improve partitioned semi-implicit FSI coupling within the classical Chorin–Témam projection framework

“…for a rigid circular cylinder. It is noticed that, a narrow lock-in range computed by [9] covers 98 Re 108, which is nearly coincident with our early work [6,12,39,51] and those of [36,[52][53][54]. On the contrary, the present method produces the widened lock-in range and the larger amplitudes during resonance.…”

“…Key aerodynamic indicators evaluated at Re = 100 are listed in Table 3, exposing that the obtained data are in better agreement with the experimental research [48]. Note that at this Re lock-in is not aroused in [54]. The cylinder oscillation is very faint when Re steps out of the lower end of the lock-in region.…”

Improving the CBS‐based partitioned semi‐implicit coupling algorithm for fluid‐structure interaction

“…These values are compared with the previously published data. 14,38,46,47 The figure is also overlaid with the famous Re − St relationship 48…”

An adaptive Fixed-Mesh ALE method for free surface flows

“…The first strategy relies in taking a time step small enough related to the mesh size so that the free surface crosses at most one element in a single time step [60]. This allows to ensure that when looking for the position of a node or integration point in the deformed mesh, it will be found in the first-layer of elements adjacent to the node or integration point, which will be locally stored in the processor owning the node.…”

“…The general formulation with details on the implementation and side ingredients like imposition of Dirichlet boundary conditions in immersed boundaries and a Lagrange Multiplier strategy for performing interpolations with restrictions can be found in [34], and its extension to fluid-structure interaction in [11,12]. More recently, the Fixed-Mesh ALE method has been used in [60] in the context of rigid bodies-fluid interaction in a parallel setting.…”