Computational study of fluid forces over a cylinder attached with elastic beam: A finite element-based simulations

In this paper, we describe numerical algorithms that can be used to solve the coupled fluid–structure interaction with incompressible viscous fluid. We characterized the fluid force effects over a circular cylinder attached to an elastic rod. To resolve the coupled governing equations, the velocity profiles are approximated with quadratic polynomials (P2), while the pressure is estimated using a different space with linear polynomials (P1) using the finite element method. The discrete systems are solved using a Newton method that employs split differences to explicitly generate the Jacobian matrices. This approach enables us to address the nonlinearities at each time step and apply direct, steady techniques. The inquiry’s findings reveal a significant relationship between the behaviors related to steady streaming and the flow regimes associated with vortex shedding. In addition, at Re = 100, steady flow is characterized by minimal displacement and negligible oscillations. In contrast, the occurrence of larger oscillations at Reynolds numbers exceeding 140 suggests an increase in flow instability.