High-order non-dissipative overset/cut-cell approach for incompressible flows

Practical turbulent flow computations require resolving a wide range of spatial and temporal scales within complex domains. High-order methods reduce the grid point requirements; however, ensuring long-time stability and discrete conservation in bounded domains remains challenging with high-order discretizations. As a result, flows in/around realistic geometries are commonly simulated using low-order schemes or artificial dissipation/numerical filters to address stability issues. This talk will present a high-order cut-cell discretization that is provably stable for linearized flow problems using non-dissipative centered schemes. The cut-cell scheme is combined with an energy-stable overset approach to simplify mesh generation and selectively refine the grid over complex/moving geometries. The proposed overset/cut-cell treatment employs a finite-difference (FD) discretization with colocated variables, which, by design, is dimensionally split. The theoretical stability proof guarantees primary and secondary conservation, and the small-cell issue is addressed by selecting flux point spacings that do not vanish even when grid points coincide at the cut-cell boundary, thus avoiding ad hoc procedures that are challenging to automate. The proposed method is applied to perform a series of inviscid and viscous incompressible flow simulations, including three-dimensional flow-induced vibration calculations over bluff bodies.