High order conservative differencing for viscous terms and the application to vortex-induced vibration flows

A new set of conservative 4th-order central finite differencing schemes for all the viscous terms of compressible Navier–Stokes equations are proposed and proved in this paper. These schemes are used with a 5th-order WENO scheme for inviscid flux and the stencil width of the central differencing scheme is designed to be within that of the WENO scheme. The central differencing schemes achieve the maximum order of accuracy in the stencil. This feature is important to keep the compactness of the overall discretization schemes and facilitate the boundary condition treatment. The algorithm is used to simulate the vortex-induced oscillations of an elastically mounted circular cylinder. The numerical results agree favorably with the experiment.