Curvilinear Moving Overset Method for High-order Non-dissipative Schemes

Abstract

This paper presents a non-dissipative, high-order, moving overset method for curvilinear grids to simulate unsteady compressible flows in complex geometries with moving components. Centered finite-difference schemes that are up to sixth-order accurate in the interior are used with a weak moving overset interface treatment. The novel aspects of the proposed approach compared to conventional overset methods are: (i) instead of overwriting all conservative or primitive variables at the interface (or fringe) points with the interpolated values, a characteristic decomposition is performed and only the incoming characteristic variables are imposed for inviscid flows, consistent with the hyperbolic character of the Euler equations; for viscous flows, the viscous fluxes are imposed in addition to the incoming characteristics variables, (ii) instead of using multiple layers of fringe points at the interface, the proposed approach ensures high-order accuracy and stability with a single layer, thus minimizing the parallel communication costs at each timestep, and (iii) the proposed approach ensures long time stability with non-dissipative schemes without introducing artificial dissipation explicitly (using numerical filters) or implicitly (using upwind schemes). The stability is demonstrated by an eigenvalue analysis of the time-dependent (semi-discrete) system matrix for moving grids, proving the eigenvalue spectra remains confined to the left half of the complex plane with grid motion. The proposed approach is validated over a range of canonical and practical unsteady flow problems involving moving grids: 1-D scalar advection, 2-D isentropic vortex convection, flow past rotating 2-D circular cylinder, pitching 2-D and 3-D airfoil/wing flow, and flow past 2-D and 3-D oscillating circular cylinder, demonstrating high-order accuracy and long time stability for inviscid/viscous flows.