Development of Unstructured Code for Rotating Zones Based on the Cabaret Method with Improved Spectral Properties

In this study we develop a modification of the high-resolution CABARET scheme for rotating meshes surrounded by an external fixed zone. CABARET is a second-order in space and time conservative/characteristic scheme with a compact stencil, which has low-dissipative and low-dispersive properties and is nonoscillatory for calculations involving nonlinear flow problems with a wide range of frequencies in computational aeroacoustics. To expand this method for the rotor-stator interaction problem, an approximation of the noninertial terms in rotating zones for conservative steps is added, and an appropriate modification of the characteristic step on the sliding interface is developed. An evolutionary approach, which ensures the preservation of the fluxes of conservative variables through the contact surface is implemented. The dispersion-improved version of the scheme with an added antidispersion term expressed via a flux derivative is added as well as a modification of the nonlinear flux correction algorithm with reduced dissipation. For testing, the problem of acoustic wave propagation through rotating zones and sliding interfaces is considered. It is shown that the developed C-ABARET method for rotating zones retains the main characteristics of the base CABARET algorithm on fixed meshes.