A three‐dimensional hybrid meshfree‐Cartesian scheme for fluid–body interaction

Abstract

SUMMARYA numerical method based on a hybrid meshfree-Cartesian grid is developed for solving three-dimensional fluid-solid interaction (FSI) problems involving solid bodies undergoing large motion. The body is discretized and enveloped by a cloud of meshfree nodes. The motion of the body is tracked by convecting the meshfree nodes against a background of Cartesian grid points. Spatial discretization of secondorder accuracy is accomplished by the combination of a generalized finite difference (GFD) method and conventional finite difference (FD) method, which are applied to the meshfree and Cartesian nodes, respectively. Error minimization in GFD is carried out by singular value decomposition. The discretized equations are integrated in time via a second-order fractional step projection method. A time-implicit iterative procedure is employed to compute the new/evolving position of the immersed bodies together with the dynamically coupled solution of the flow field. The present method is applied on problems of free falling spheres and tori in quiescent flow and freely rotating spheres in simple shear flow. Good agreement with published results shows the ability of the present hybrid meshfree-Cartesian grid scheme to achieve good accuracy. An application of the method to the self-induced propulsion of a deforming fish-like swimmer further demonstrates the capability and potential of the present approach for solving complex FSI problems in 3D.

Experiments on fall of open tori

“…Some experiments are performed for investigating the eect of such an initial angle showing that the nal descent mode is not aected as long as the initial angle is not "too large". A similar behavior has been observed in experimental studies of falling thin disks [3,33], thick disks [34] and also in numerical simulations on a falling torus released with an initial angle of 30 • [21]. Eect of an initial angle is illustrated in Fig.…”

“…For this low Re range, never reached during the present study, the rings underwent a steady vertical translation. The same motion is reported in the numerical work of Yu et al [21] for a torus of aspect ratio of 2 falling at Re = 25 or 50, and a detached axisymmetric recirculation bubble forms in the wake. This study also showed that when the torus is released with an angle of 30 • it returns to the horizontal (0 • ) after a few damped oscillations.…”

Forward flight and sideslip manoeuvre of a model hawkmoth

“…The standard seven-point central finite difference scheme is applied at Cartesian grid nodes that do not have mesh-free nodes nearby, while the singular value decomposition-generalized finite difference (SVD-GFD) scheme is applied at the mesh-free nodes and Cartesian nodes with mesh-free nodes nearby. Solutions by this scheme have been discussed in detail by Chew, Yeo & Shu (2006), Wang et al (2008Wang et al ( , 2010, Yu et al (2011) and Zhang (2013). The configuration of the nodal mesh around the model hawkmoth is shown in figure 31(a).…”

An Application of GPU Acceleration in CFD Simulation for Insect Flight

“…The system may become under-determined when the small singular values were omitted, but the SVD method ensures a solution with minimum L 2 error can be obtained. The SVD scheme with regularization has been found to be robust and accurate in the practice of 3D simulations for natural flyers and swimmers [11,17,18]. …”