Low-Reynolds-number flow around an oscillating circular cylinder using a cell viscousboundary element method

Abstract

Flow fields from transversely oscillating circular cylinders in water at rest are studied by numerical solutions of the two-dimensional unsteady incompressible Navier-Stokes equations adopting a primitive-variable formulation. These findings are successfully compared with experimental observations. The cell viscous boundary element scheme developed is first validated to examine convergence of solution and the influence of discretization within the numerical scheme of study before the comparisons are undertaken. A hybrid approach utilising boundary element and finite element methods is adopted in the cell viscous boundary element method. That is, cell equations are generated using the principles of a boundary element method with global equations derived following the procedures of finite element methods. The influence of key parameters, i.e. Reynolds number Re, Keulegan-Carpenter number KC and Stokes' number beta, on overall flow characteristics and vortex shedding mechanisms are investigated through comparisons with experimental findings and theoretical predictions. The latter extends the study into assessment of the values of the drag coefficient, added mass or inertia coefficient with key parameters and the variation of lift and in-line force results with time derived from the Morison's equation. The cell viscous boundary element method as described herein is shown to produce solutions which agree very favourably with experimental observations, measurements and other theoretical findings