Analysis of non-conservative interpolation techniques in overset grid finite-volume methods

Abstract This paper reports on the challenges of using an overset grid approach when simulating incompressible flows with a cell-centred finite-volume solver. The focal point is on the grid coupling approach. Usually, overset grid methods for unstructured three-dimensional grids apply a local interpolation of field values onto the partner grid as a coupling procedure. Such local interpolation is obviously insufficient to guarantee that the global sum of the mass fluxes across the overlapping interfaces vanishes. Hence, the inherent mass conservation of finite volume methods is violated by the non-conservative property of the overset grid coupling. Since incompressible finite-volume solvers directly use the mass defect when solving for the pressure, severe pressure fluctuations may be provoked. A sensitivity study of the residual mass defect on overlapping grids and the related pressure fluctuations is performed for a variety of coupling strategies. Emphasis is given to five different aspects, i.e. relative grid motion, the order of accuracy of the employed baseline interpolation, the formulation of global mass conservation enforcing practices, the resolution quality of the overlapping grids and multiphase-flow issues. Examples included refer to a simple 2D cylinder flow, a 2D/3D lid-driven cavity flow, a 2D body force disturbed channel flow and 2D oscillating hydrofoil flows in fully wetted single-phase and immiscible two-phase conditions. Results reveal that transient flows and simulations with relative grid motion are subject to significant mass and pressure fluctuations. High-order interpolation and grid refinement prove beneficial, but can still be afflicted with severe disturbances, particularly when the resolution properties of the overlapping grids disagree. Two-phase flows with a high density ratio show a distinct compensating behaviour, while the introduction of flux or wetted volume correction practices leads to notable improvements for single-phase flows in both homogeneous and heterogeneous resolution conditions.