An Edge-Based Smoothed Finite-Element Method for Vortex-Induced Vibration in Generalized Newtonian Fluids

Application or an edge-based smoothed finite-element method (ESFEM) to vortex-induced vibration (VIV) or a circular cylinder in generalized Newtonian fluids is presented. The incompressible Navier-Stokes equations incorporating power-law and Carreau-Yasuda viscosity models are solved by the characteristic-based split scheme under the arbitrary Lagrangian-Eulerian description. The equation of motion of an elastically supported circular cylinder subjected to the generalized Newtonian fluid flows is advanced via the generalize-a method. The spatial discretization is based on a three-node triangular element that is particularly suitable for the ESFEM. New integration points are subsequently proposed in local smoothing domains to facilitate the weak-form approximation. The fluidic excitation acting on the submerged cylinder is also derived from the edge-based notion. Grid nodes are instantaneously rearranged by a cost-effective moving submesh approach. Especially, a mass source term is structured in the current context to satisfy geometric conservation law for the ESFEM. The tightly coupled mechanical system is settled through fixed-point iterative procedure. The present method is validated against available data for two non-Newtonian VIV examples. (C) 2022 American Society of Civil Engineers.

Automated summary

This paper presents the application of an edge-based smoothed finite-element method (ESFEM) to study vortex-induced vibration (VIV) of a circular cylinder in generalized Newtonian fluids. The incompressible Navier-Stokes equations, incorporating power-law and Carreau-Yasuda viscosity models, are solved using a characteristic-based split scheme under the arbitrary Lagrangian-Eulerian description. The equation of motion for an elastically supported circular cylinder subjected to the flow of the generalized Newtonian fluid is derived using the generalize-a method. The discretization of space is based on a three-node triangular element, which is particularly suitable for ESFEM. New integration points are proposed in local smoothing domains to improve the weak-form approximation. The fluidic excitation acting on the submerged cylinder is also determined based on the edge-based notion. Grid nodes are rearranged using a cost-effective moving submesh approach. A mass source term is included in the current context to satisfy the geometric conservation law for ESFEM. The tightly coupled mechanical system is solved using a fixed-point iterative procedure. The validity of the proposed method is demonstrated through the comparison with available data for two non-Newtonian VIV examples.