AbstractApplication of an edge-based smoothed finite-element method (ESFEM) to vortex-induced vibration (VIV) of 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-α 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.