An Immersed Boundary Method for pressure-based compressible solvers with applications to free-convection flows, acoustic wave propagation and thermal plasma
Résumé
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 simula-
tions 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 remov-
ing 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 classi-
cal projection methods for incompressible flows, our objective in this paper is
to present an adaptation of an efficient and accurate IBM developed for an in-
compressible 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 vari-
able 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.
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