Element-Quality-Based Stiffening for the Pseudoelastic Mesh-Moving Technique

Abstract

In this study, element-quality-based stiffening (EQBS) was developed as a method of maintaining mesh quality in the pseudoelastic mesh-moving technique. The proposed EQBS technique increases the stiffness of the element based on two element quality parameters, the element area and shape; this differs from techniques used in previous studies. Importantly, EQBS includes the previously proposed Jacobian-based stiffening (JBS) and minimum height-based stiffening (MHBS) techniques as a specific case. Therefore, it is quite general scenario of the selective stiffening of the mesh. The proposed EQBS technique was applied to the mesh-moving of a rectangular domain including a structure consisting of a square and a fin that undergo large translations and rotations. The proposed EQBS technique showed better performance than JBS on test problems with large translations and rotations applied to the structure. This is because EQBS considers the shear deformation of the element in addition to the tensile and compressive deformations.

Computational fluid–structure interaction framework for passive feathering and cambering in flapping insect wings

“…In general, the interface tracking methods need sophisticated mesh control methods based on implicit algorithms, of which computational cost might be same with or more expensive than that of CFD and CSD solvers. 27,[63][64][65][66] Furthermore, realistic structural mechanics models that are intended to replicate structural details using finite elements seem to be too expensive computationally to be implemented into strongly coupled FSI simulations. 13 Hence, to our best knowledge, there is no model wing that can reproduce both cambering and feathering passively, of which magnitudes are equivalent to those of actual insects, from large elastic deformations in the FSI simulations.…”

“…Then, the computational cost for the mesh control tends to be more expensive than those for solving the consistent PPE and equilibrium equations. 65 In this study, for the purpose of eliminating this numerical difficulty, we propose a novel approach that combines a pixel model wing with an explicit mesh control method. The pixel model wing is based on the shape simplification of insect flapping wings, 74 but different from the previous study, it is represented as the structured mesh with pixel modeling of veins using shell finite elements.…”

“…If the pixel model wing is applied to the three-dimensional FSI analysis, numerical simulation of the FSI for feathering and cambering becomes feasible in a typical computational environment because the computational cost can be drastically reduced. For example, robust mesh-moving techniques for complex finite element meshes [63][64][65][66] will not be necessary.…”

“…FSI simulations with passive feathering and cambering of which magnitudes are equivalent to those of actual insects are still challenging for IB methods and partitioned FSI procedures with both interface capturing and tracking because of the large added mass effects, the large body motions, and the large elastic deformations. In general, the interface tracking methods need sophisticated mesh control methods based on implicit algorithms, of which computational cost might be same with or more expensive than that of CFD and CSD solvers 27,63–66 . Furthermore, realistic structural mechanics models that are intended to replicate structural details using finite elements seem to be too expensive computationally to be implemented into strongly coupled FSI simulations 13 .…”

Performance evaluation of the pixel wing model for the insect wing's camber

“…In these models, the complicated network of the veins is represented using the beam elements, and the wing membrane is represented using the unstructured elements. However, the usage of the unstructured elements might impose a sophisticated mesh-moving technique on controlling the fluid mesh surrounding the wing model [9] in the finite element analysis of the fluid-structure interaction. Hence, for the purpose of computational efficiency, the pixel wing model consisting of a structured mesh using shell elements has been proposed [10].…”