Prandtl-Glauert-Lorentz based Absorbing Boundary Conditions for the convected Helmholtz equation

Hélène Barucq (1) , Nathan Rouxelin (1) , Sébastien Tordeux (1)

1 MAKUTU - Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes

We construct Absorbing Boundary Conditions (ABCs) for the convected Helmholtz equation. The construction is based upon the Prandtl-Glauert-Lorentz map which transforms the convected Helmholtz equation into the regular Helmholtz equations. The new ABCs are thus issued from classical Engquist-Majda ABCs and are valid for carrier flows that vary inside the domain but become uniform at infinity. They lead to accurate numerical results for low and intermediate Mach numbers and are easy to implement in an existing finite element or discontinuous Galerkin solver.

Mots clés: Convected Helmholtz equation; Absorbing Boundary Conditions; ABC; Prandtl Glauert Lorentz transformation

Domaines: Analyse numérique [math.NA]

Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux. Prandtl-Glauert-Lorentz based Absorbing Boundary Conditions for the convected Helmholtz equation. 2021. ⟨hal-03288930v1⟩