A conservative viscous vorticity method for unsteady unidirectional and oscillatory flow past a circular cylinder

Abstract

A conservative vorticity method for solving the 2-D incompressible unsteady viscous flow in the eulerian frame is proposed. The numerical method implements the vorticity-stream function formulation of the Navier–Stokes (N–S) equations, solved by the cell-centered Finite Volume Method (FVM). A convection limiter, coupling the first order upwind scheme and the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme, is introduced to maintain the accuracy and keep the monotonicity of vorticity interpolations. The vorticity induced stream functions are recovered by a closed-form expression, which also accurately predicts the far-field boundary conditions. The convective flux is evaluated by the difference of stream functions on the neighboring two nodes, which spontaneously eliminates the net mass flux out of a control cell. The conservative FVM and QUICK scheme and the definite evaluations of stream functions and convective flux guarantee the conservation of circulation and mass. The impulsively started flow past a circular cylinder at Reynolds numbers ranging from 100 to 9500 and the inline oscillatory flow around a circular cylinder at Reynolds numbers 100 and 200 are numerically simulated using this method. The current results under the inertial and non-inertial translational frame are well validated by comparisons with other numerical and experimental benchmark tests.