Role of solution reconstruction in hypersonic viscous computations using a sharp interface immersed boundary method

This work discusses the development of a sharp interface immersed boundary (IB) method for viscous compressible flows and its assessment for accurate computations of wall shear and heat fluxes in hypersonic flows. The IB method is implemented in an unstructured Cartesian finite-volume (FV) framework and resolves the geometric interface sharply on the nonconformal mesh through direct imposition of boundary conditions employing a local reconstruction approach. The efficacy of the IB-FV solver is investigated for canonical high-speed viscous flows over a range of Mach numbers. The numerical results indicate that the surface pressure and shear stress distributions are computed with reasonable accuracy, whereas surface heat fluxes for aerodynamically blunt configurations are underpredicted. Employing a set of carefully designed experiments and simple diagnostic tools, we probe the possible causes for the underprediction in heat flux. We show that there exist two sources of error - one due to grid resolution and the other due to solution reconstruction, with the latter being more prominent and responsible for the observed underprediction in heat fluxes. Studies reveal that the heat flux estimates are sensitive to the choice of temperature reconstruction and linear interpolations could lead to poor estimates of heat flux. Our investigations conclusively point out the fact that existing polynomial-based reconstruction approaches for sharp interface IB techniques are not necessarily adequate for heat transfer predictions in high Reynolds number hypersonic flows.