Non-Dissipative Moving Overset Grid Framework for Unsteady Aerodynamics

Flow-structure interactions in applications, such as bio-inspired flight, wing flutter, and rotor flows, are driven by transient vortical structures that interact, merge, and reorganize. Accurately resolving the dynamics of these flow structures is key to understanding and predicting the aerodynamic performance in those applications. The wide range of spatial and temporal scales motivates the use of high-order non-dissipative methods in computational studies. Moreover, moving-body flow problems are commonly handled using body-conforming overset grids due to their flexibility in managing complex, multi-body configurations. Existing unsteady flow simulations using overset grids typically require artificial dissipation or low-pass spatial filtering to ensure long-time numerical stability. Such treatments can nonphysically alter critical flow features and dampen vortical structures and shear turbulence in the wake. A high-order scheme without any artificial dissipation avoids undesirable damping, thereby helping obtain an accurate resolution of the flow structures. This paper proposes and investigates a high-order non-dissipative moving overset grid approach in a generalized curvilinear coordinate system to analyze the flow structures and mechanisms underlying highly unsteady aerodynamic interactions. The approach employs a sixth-order central scheme in the interior with a summation-by-parts (SBP) boundary closure yielding a fourth-order accurate scheme globally. The overset grid interfaces are treated without artificial dissipation, implementing a simultaneous approximation term (SAT) penalty approach with a characteristic decomposition. The developed framework has been extensively tested for various inviscid and viscous moving body/grid problems. The long-time stability and accuracy are established by simulating the inviscid convecting vortex flow problem over a moving 2-D overset grid without any filters or numerical dissipation. Further, 2-D and 3-D pitching-heaving airfoil/wing flow simulations are performed to evaluate the robustness for viscous flow problems. The quantitative validation of these flow cases, along with a few results from rotor flow simulations obtained using the framework, is discussed.