Immersed boundary conditions for hypersonic flows using ENO-like least-square reconstruction

Abstract

In this study, we present an immersed boundary reconstruction method for the simulation of viscous compressible flows presenting strong discontinuities in the vicinity of the immersed body. The technique we propose is based on a weighted least-square reconstruction. Its major feature is that the weights are automatically adapted to the presence of a discontinuity within the least-square stencil by using a shock-sensor approach. In so doing, the reconstruction becomes ENO-like and mathematically consistent even in the presence of strong discontinuities. The objective of this paper is to demonstrate that it then becomes possible to use an immersed boundary method for the simulation of hypersonic flows and that it is robust, even for flows around complex geometries. To do so, two-dimensional compressible Navier-Stokes equations are solved to study canonical hypersonic flows and it is showed that the results are in good agreement with either experimental data and/or body-fitted approaches and that the impact of the immersed boundary technique on the overall spatial order of convergence is reasonable.