Development of the Recursive Convolutional CFS-PML for the Wave-Equation-Based Meshless Method

Wang, Junfeng; Chen, Zhizhang; Peng, Cheng; Li, Jinyan; Ponomarenko, Sergey A.

doi:10.1109/tap.2020.3037673

Cited by 8 publications

(3 citation statements)

References 27 publications

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“…Different PML techniques have been proposed, such as the convolution PML 39 and the CFS-PML. 40,41 In the present analysis, the CFS-PML technique is implemented in an unsplit form to overcome the limitations of long-time instability. In former researches, the CFS-PML is based on the first-order wave equations and their formulas are not suitable for the nonlinear acoustic model in a moving frame.…”

Section: Governing Equationsmentioning

confidence: 99%

“…For the computation of exterior acoustics, the perfectly matched layers (PMLs) are introduced to truncate an unbounded fluid domain into a bounded one. Different PML techniques have been proposed, such as the convolution PML 39 and the CFS‐PML 40,41 . In the present analysis, the CFS‐PML technique is implemented in an unsplit form to overcome the limitations of long‐time instability.…”

Section: Nonlinear Acoustic Waves In Moving Frame Of Referencementioning

confidence: 99%

“…For a two‐dimensional problem, Equation (4a) can be rewritten based on a stretched complex coordinate applied in the x 1 ‐direction, given as:

\mathrm{i}\omega {\rho}_{\mathrm{F}}^{\prime }+{\rho}_{\mathrm{F}0}\left[\frac{1}{s_1}\frac{\partial }{\partial {x}_1}\left(\frac{1}{s_1}\frac{\partial }{\partial {x}_1}\right)+\frac{\partial }{\partial {x}_2}\frac{\partial }{\partial {x}_2}\right]\varphi =0,

{s}_1=1+\frac{\sigma_1}{\mathrm{i}\omega +{\alpha}_1},

where

{s}_1

is the stretched‐coordinate factor 40 .

{\sigma}_1

and

{\alpha}_1

are parameters for the CFS‐PMLs, and their expressions can be referred to Reference 41. The stretched term in Equation (5a) is mainly concerned, which can be further expressed as:

\begin{matrix} lefttrue \\ \frac{1}{s_{1}} \frac{\partial}{\partial x_{1}} (\frac{1}{s_{1}} \frac{\partial}{\partial x_{1}}) φ & = φ_{, 11} - \frac{1}{((), α_{1} goodbreak+ normali ω goodbreak+ σ_{1})} () \end{matrix}

…”

Section: Nonlinear Acoustic Waves In Moving Frame Of Referencementioning

confidence: 99%

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Implicit coupling methods for nonlinear interactions between a large‐deformable hyperelastic solid and a viscous acoustic fluid of infinite extent

Li,

Qu,

Meng

2023

Numerical Methods in Fluids

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This paper addresses the challenges in studying the interaction between high‐intensity sound waves and large‐deformable hyperelastic solids, which are characterized by nonlinearities of the hyperelastic material, the finite‐amplitude acoustic wave, and the large‐deformable fluid–solid interface. An implicit coupling method is proposed for predicting nonlinear structural‐acoustic responses of the large‐deformable hyperelastic solid submerged in a compressible viscous fluid of infinite extent. An arbitrary Lagrangian–Eulerian (ALE) formulation based on an unsplit complex‐frequency‐shifted perfectly matched layer method is developed for long‐time simulation of the nonlinear acoustic wave propagation without exhibiting long‐time instabilities. The solid and acoustic fluid domains are discretized using the finite element method, and two different options of staggered implicit coupling procedures for nonlinear structural‐acoustic interactions are developed. Theoretical formulations for stability analysis of the implicit methods are provided. The accuracy, robustness, and convergence properties of the proposed methods are evaluated by a benchmark problem, that is, a hyperelastic rod interacting with finite‐amplitude acoustic waves. The numerical results substantiate that the present methods are able to provide long‐time steady‐state solutions for a nonlinear coupled hyperelastic solid and viscous acoustic fluid system without numerical constraints of small time step sizes and long‐time instabilities. The methods are applied to investigate nonlinear dynamic behaviors of coupled hyperelastic elliptical ring and acoustic fluid systems. Physical insights into 2:1 and 4:2:1 internal resonances of the hyperelastic elliptical ring and period‐doubling bifurcations of the structural and acoustic responses of the system are provided.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Nonlinear Acoustic Waves In Moving Frame Of Referencementioning

confidence: 99%

“…For a two‐dimensional problem, Equation (4a) can be rewritten based on a stretched complex coordinate applied in the x 1 ‐direction, given as:

\mathrm{i}\omega {\rho}_{\mathrm{F}}^{\prime }+{\rho}_{\mathrm{F}0}\left[\frac{1}{s_1}\frac{\partial }{\partial {x}_1}\left(\frac{1}{s_1}\frac{\partial }{\partial {x}_1}\right)+\frac{\partial }{\partial {x}_2}\frac{\partial }{\partial {x}_2}\right]\varphi =0,

{s}_1=1+\frac{\sigma_1}{\mathrm{i}\omega +{\alpha}_1},

where

{s}_1

is the stretched‐coordinate factor 40 .

{\sigma}_1

and

{\alpha}_1

are parameters for the CFS‐PMLs, and their expressions can be referred to Reference 41. The stretched term in Equation (5a) is mainly concerned, which can be further expressed as: