An explicit characteristic-based immersed boundary method for compressible flows

In this work, characteristic-based volume penalization is combined with a high-order energy-stable finite difference framework for both the compressible Navier-Stokes and Euler equations. The method is purely explicit where free parameters are chosen based on the limitations of the underlying discretization. This results in a computationally efficient method that avoids increased stiffness associated with the boundary treatment and consequently does not rely on iterative solvers for improved stability. To improve robustness in the presence of strong discontinuities (e.g. shocks), a regularized Heaviside function is imposed on the volume penalization terms near the interface. Unlike other immersed boundary methods applied to compressible flows, the proposed method does not require modifications to the underlying computational stencil. The method is demonstrated on a series of inviscid and viscous, subsonic and supersonic flows. (C) 2021 Elsevier Inc. All rights reserved.