Second-order interpolation techniques for accurate surface data estimation in immersed-boundary methods

Immersed-Boundary Methods (IBM) enable the use of Cartesian grids that do not conform to the shape of the body, past which flow is simulated. As a consequence, data at the immersed surface is not directly retrievable from the grid. Suitable interpolation methods have to be employed for data reconstruction at the surface. The authors of the present work have previously worked with first-order inverse-distance based interpolation methods and have applied them to turbulent flow past NACA 16009 airfoil (Bharadwaj S, A., Ghosh, S., and Joseph, C., "Interpolation Techniques for Data Reconstruction at Surface in Immersed Boundary Method," 55th AIAA Aerospace Sciences Meeting, 2017, p. 1427). In the present work, second-order methods of interpolation for drag prediction, are presented with the motive of improving the accuracy of the predictions (compared to the first-order methods) and to investigate if these methods can produce accurate surface data even when the solution is obtained from relatively coarse grids. Investigations have been performed on three flow cases: Mach 0.5 laminar flow past a flat plate, Mach 0.5 laminar flow past NACA 0012 airfoil, and Mach 0.2 turbulent flow past a flat plate. It is observed that, in general, the second-order methods improve the accuracy of drag predictions at the surface (compared to the first-order methods) and are found to be accurate even when applied to coarse grid simulations.