Large eddy simulation using a new set of sixth order schemes for compressible viscous terms

A set of conservative sixth order central differencing schemes is suggested for compressible flows with variable viscosity coefficient. This new set of central differencing schemes has the stencil width matching that of the seventh order weighted essentially non-oscillatory scheme (WENO). This feature is important to maintain the compactness of the seventh order WENO scheme and facilitate boundary condition treatment. As an application example, a large eddy simulation (LES) is conducted for a cylinder flow using the seventh order WENO scheme for the convective terms and the new set of sixth order central differencing scheme for the viscous terms. The results are compared with those from other research groups and those obtained using the fifth order WENO scheme and fourth order central differencing.