Data reconstruction at surface in immersed-boundary methods

Abstract

This work compares interpolation techniques for data reconstruction at the surface in an immersed-boundary method. Three different methods of surface pressure reconstruction based on inverse distances are presented, which are christened as: Inverse Distance Weight (IDW) method, Inverse Distance Weight at Interpolation Point method (IDW-IP) and Inverse Distance Weight based on Upwinding (IDW-Upwind) method. Additionally, shear stress at the immersed surface is determined using two approaches: direct interpolation of velocity gradient at the surface using IDW method, and interpolation of velocity at a point along the surface normal using IDW-IP method. The interpolation methods are verified against analytic solutions of ideal flow past a circular cylinder and subsonic-supersonic inviscid flow in a convergent-divergent nozzle, and validated against laminar flow simulations of Mach 0.5 flow past a NACA0012 airfoil, Mach 2.0 flow past a circular cylinder, and Mach 3.0 flow past a 10∘ ramp. The verification cases show that while the pressure values reconstructed at the surface by the three interpolation methods are very similar for the incompressible flow, the IDW-Upwind method produces the sharpest pressure rise across the normal shock in the convergent-divergent nozzle. Comparisons of the reconstructed surface pressure coefficient (Cp) and skin-friction coefficient (Cf) with values available from literature or ANSYS-Fluent simulations conducted as part of the validation study show good match, but indicate that the reconstructed pressure and shear stress values at the immersed surface has noise, which, however, reduces with grid refinement. Further, the IDW and IDW-Upwind method for pressure reconstruction, and the gradient reconstruction based method for shear stress calculation are shown to produce less noise in computed values. Integrated drag and lift values using the reconstructed surface pressure and shear stress indicate that while the different methods used for pressure reconstruction result in similar values of aerodynamic loads, the gradient-based shear stress calculations result in more accurate load estimation. Finally, one of the interpolation methods (IDW-Upwind) is used to investigate the variation of the surface pressure coefficient with time for a NACA0012 airfoil undergoing non-periodic plunge motion in a Mach 0.2 flow. The computed surface pressure coefficients are correlated with the leading and trailing edge vortices in the flow field.