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

Barucq, Hélène; Rouxelin, Nathan; Tordeux, Sébastien

doi:10.1016/j.jcp.2022.111450

Cited by 7 publications

(3 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mentioned approach has been utilized extensively in various studies. For instance, Barucq et al [41] analyzed the Helmholtz equation numerically by using ABC. They conducted an in-depth analysis of the impact of various parameters on these numerical results.…”

Section: Introductionmentioning

confidence: 99%

Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

Yang,

Liu,

Chen

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

The modified second-grade fluid flow across a plate of semi-infinite extent, which is initiated by the plate’s movement, is considered herein. The relaxation parameters and fractional parameters are introduced to express the generalized constitutive relation. A convolution-based absorbing boundary condition (ABC) is developed based on the artificial boundary method (ABM), addressing issues related to the semi-infinite boundary. We adopt the finite difference method (FDM) for deriving the numerical solution by employing the L1 scheme to approximate the fractional derivative. To confirm the precision of this method, a source term is added to establish an exact solution for verification purposes. A comparative evaluation of the ABC versus the direct truncated boundary condition (DTBC) is conducted, with their effectiveness and soundness being visually scrutinized and assessed. This study investigates the impact of the motion of plates at different fluid flow velocities, focusing on the effects of dynamic elements influencing flow mechanisms and velocity. This research’s primary conclusion is that a higher fractional parameter correlates with the fluid flow. As relaxation parameters decrease, the delay effect intensifies and the fluid velocity decreases.

show abstract

Section: Introductionmentioning

confidence: 99%

Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

Yang,

Liu,

Chen

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…We will use simple ABCs including the dissipative component, derived in appendix, since it seems that very little work has been proposed on that topic. Only recently, Barucq et al [54] designed ABCs in the context of 3D atmospheric waves, whose model contains a damping term. Our 1D and 2D results are consistent with the ABCs derived in [54].…”

Section: Introductionmentioning

confidence: 99%

“…Only recently, Barucq et al [54] designed ABCs in the context of 3D atmospheric waves, whose model contains a damping term. Our 1D and 2D results are consistent with the ABCs derived in [54].…”

Section: Introductionmentioning

confidence: 99%

TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media

Graff

Cullen

2023

Inverse Problems

View full text Add to dashboard Cite

We propose to explore the Time-Reversed Absorbing Condition (TRAC) method in the case of dissipative homogeneous media. In previous work, the TRAC method was derived from the time-reversibility of the (undamped) wave equation and proved to be efficient in both the time domain and the frequency domain. Namely, two main utilisations of the TRAC method have been probed: (a) redatuming, i.e., moving virtually the measurements by reconstructing the wavefield and (b) tracking down the location of a possible inclusion inside the domain.In this paper, we focus on the redatuming application and investigate the feasibility of the TRAC method in the case of dissipation. In particular, we will see that performing the classical TRAC method, i.e., ignoring the dissipation, may give satisfactory results, even for larger values of dissipation.An analysis is provided in the frequency-domain and one-space dimension and shows satisfactory updated versions of the TRAC method. Moreover, a systematic error study in two-space dimension is illustrated via numerical examples.

show abstract

Numerical solution of convected wave equation in free field using artificial boundary method

Wang,

et al. 2024

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we propose two procedures focusing on the computation of the time‐dependent convected wave equation in a free field with a uniform background flow. Both procedures are based on a framework, expended from Du et al. (SIAM J. Sci. Comput. 40 (2018), A1430–A1445.), of constructing the Dirichlet‐to‐Dirichlet (DtD)‐type discrete absorbing boundary conditions (ABCs). The first procedure is dedicated to reducing the infinite problem into a finite problem by a direct application of the framework on the finite difference discretization of the convected wave equation. However, the presence of convection terms makes the stability analysis hard to implement, which motivates us to develop the second procedure. First, the convected wave equation is transformed into a standard wave equation by using the Prandtl‐Glauert‐Lorentz transformation. After that, we obtain the DtD‐type ABC by using the above framework, and on this basis, derive an equivalent Dirichlet‐to‐Neumann‐type ABCs, which makes stability and convergence analysis easy to be obtained by the classical energy method. The effectiveness and comparison of these two procedures are investigated through numerical experiments.

show abstract

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

Cited by 7 publications

References 31 publications

Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media

Numerical solution of convected wave equation in free field using artificial boundary method

Contact Info

Product

Resources

About