CABARET on rotating meshes

Abstract

The Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) method for 3D gas dynamics equations is generalised to rotating hexahedral mesh zones using the sliding interface approach, which extends applications of the original algorithm to a wide range of unsteady rotor flow problems. Important properties of the suggested extension of the CABARET scheme include the preservation of good linear dispersion and dissipation properties of the original CABARET method on fixed grids. To strictly preserve flux conservation at the sliding interface, the so-called supermesh approach is implemented that uses the projection of the contact faces on both sides of the sliding interface onto an intermediate virtual surface. The implementation is based on applying the sub-cell and sub-face solution reconstruction on the sliding interface of hexahedral meshes rather than deforming unstructured meshes. The sub-faces are defined by constructing projection overlap polygons using the Sutherland-Hodgman clipping algorithm. A local characteristic flux splitting is applied at each overlap polygon face, while updating the local stencil connectivity table at each time step. To further improve the dispersion properties of the CABARET grid at small Courant–Friedrichs–Lewy numbers, the dispersion-improved version of the CABARET method previously developed on rectangular Cartesian meshes is extended to non-uniform curvilinear meshes typical of open-rotor applications. Numerical examples are provided for the analytical problem of normal acoustic wave propagation through a rotating cylindrical grid zone embedded in an outer stationary grid. The error decay rates are calculated and compared with the theoretical order of CABARET convergence. In addition, the same algorithm accelerated on Graphics Processing Units (GPUs) is applied for simulations the flow around a generic two-bladed rotor in hover in the Wall Model Large Eddy Simulation framework. For the latter case, flow solutions are analysed, and their numerical grid sensitivity is discussed.