Stable Perfectly Matched Layers with Lorentz transformation for the convected Helmholtz equation

Abstract

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On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

“…The cubic-quintic nonlinear non-paraxial pulse propagation model accounts for the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. The Khater approach is employed to observe some new exact traveling wave solutions to the cubic-quintic nonlinear non-paraxial pulse propagation model (NPPP) equation (Li and Wang 2021;Marchner et al 2021).…”

Construction and Numerical Assessment of Local Absorbing Boundary Conditions for Heterogeneous Time-Harmonic Acoustic Problems

“…A second issue for convected problems is the presence of inverse modes that makes the PML unstable and ineffective in practice. Fortunately stabilization techniques are available and we will use the stabilized version of the PML described in [63]. The strategy to compute the reference solution is illustrated in ∂ In order to evaluate the efficiency of the ABCs we consider a set of frequencies and ABC positions L for a given mode n. The selected frequencies span the elliptic, grazing and hyperbolic regimes.…”

“…As a result we obtain a reference solution that has the precision of the DtN map, and by linearity we suppose it holds in the multi-modal case. Additional considerations can be found in the appendix of [63]. For the simulations we use again Q4 elements of size h = 1/40 and set the p-FEM order to p = 6.…”

Low-order Prandtl-Glauert-Lorentz based Absorbing Boundary Conditions for solving the convected Helmholtz equation with Discontinuous Galerkin methods

“…In [BDL04], stabilized PMLs have been derived for the time-harmonic convected Helmholtz equation in a duct with a uniform flow, adapting ideas formerly developed in [HN02] and [Hu01] for time-dependent problems. In a very recent work [MBAG21], Marchner et al have proposed a stabilized PML for the convected Helmholtz equation following the approach in [DDMT11] of applying the Prandtl-Glauert-Lorentz transformation (PGL) to remove the external flow to end up with the standard Helmholtz equation for which stable PMLs exist. It is worth noting that in [DDMT11], the PML is constructed for the advective acoustic equation when the velocity of the fluid is parallel to a particular direction while [MBAG21] only assumes the flow is uniform and subsonic.…”

“…In a very recent work [MBAG21], Marchner et al have proposed a stabilized PML for the convected Helmholtz equation following the approach in [DDMT11] of applying the Prandtl-Glauert-Lorentz transformation (PGL) to remove the external flow to end up with the standard Helmholtz equation for which stable PMLs exist. It is worth noting that in [DDMT11], the PML is constructed for the advective acoustic equation when the velocity of the fluid is parallel to a particular direction while [MBAG21] only assumes the flow is uniform and subsonic. In this paper, we focus on the construction of ABCs for the convected Helmholtz equation which can be implemented easily in the different HDG formulations that we have introduced in a previous work [BRT21].…”