An Immersed Boundary Method for pressure-based compressible solvers with applications to free-convection flows, acoustic wave propagation and thermal plasma

Abstract

Immersed Boundary Methods (IBM) are a practical class of methods that enable fluid computations in complex geometry while keeping a structured mesh. Most of the existing IBM have been developed in the framework of incompressible solvers, despite their significant interest to perform simulations in more complex configurations requiring a compressible solver. In the last years, pressure-based solvers met a growing interest to perform numerical simulations of compressible flows, due to their attractive features, as removing the stability condition on the acoustic time step, and being asymptotically preserving of the incompressible regime when the Mach number tends to zero. As this class of compressible solvers share many common features with classical projection methods for incompressible flows, our objective in this paper is to present an adaptation of an efficient and accurate IBM developed for an incompressible solver by Ng et al. in [1] to a pressure-based compressible solver recently published by Urbano et al. in [2]. The proposed algorithm benefits of the attractive properties of the original IBM proposed in [1] while being able to undertake simulations in much more complex configurations. In particular, we will present validations and illustrations of the proposed solver in various configurations as free-convection flows, acoustic waves propagating in a variable section pipe or interacting with a solid obstacle, as well as the description of a thermal plasma during an electric arc discharge in a gas.