scholarly journals The heterogeneous Helmholtz problem with spherical symmetry: Green’s operator and stability estimates

2020 ◽  
pp. 1-37
Author(s):  
Stefan Sauter ◽  
Céline Torres
Keyword(s):  
Wave Propagation ◽  
Helmholtz Equation ◽  
Frequency Domain ◽  
Spherical Symmetry ◽  
Wave Speed ◽  
Heterogeneous Media ◽  
Stability Estimates ◽  
Green’S Operator ◽  
Helmholtz Problem ◽  
Explicit Representations

We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and will derive explicit representations of the Green’s operator and stability estimates which are explicit in the frequency and the wave speed.

scholarly journals Wavenumber explicit convergence analysis for finite element discretizations of general wave propagation problems

2019 ◽  
Vol 40 (2) ◽  
pp. 1503-1543 ◽  
Author(s):  
T Chaumont-Frelet ◽  
S Nicaise
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Helmholtz Equation ◽  
Error Estimates ◽  
Heterogeneous Media ◽  
Harmonic Wave ◽  
Stability Conditions ◽  
Full Generality ◽  
Finite Element Discretizations ◽  
Element Discretizations

Abstract We analyse the convergence of finite element discretizations of time-harmonic wave propagation problems. We propose a general methodology to derive stability conditions and error estimates that are explicit with respect to the wavenumber $k$. This methodology is formally based on an expansion of the solution in powers of $k$, which permits to split the solution into a regular, but oscillating part, and another component that is rough, but behaves nicely when the wavenumber increases. The method is developed in its full generality and is illustrated by three particular cases: the elastodynamic system, the convected Helmholtz equation and the acoustic Helmholtz equation in homogeneous and heterogeneous media. Numerical experiments are provided, which confirm that the stability conditions and error estimates are sharp.

scholarly journals Non-local variant of the Optimised Schwarz Method for arbitrary non-overlapping subdomain partitions

2020 ◽  
Author(s):  
Xavier Claeys
Keyword(s):  
Wave Propagation ◽  
Helmholtz Equation ◽  
Scalar Wave ◽  
Schwarz Method ◽  
Local Variant ◽  
New Variant ◽  
Helmholtz Problem ◽  
Non Local

We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new variant of the Optimized Schwarz Method (OSM) that remains valid in the presence of cross-points in the subdomain partition. This leads to the derivation of a strongly coercive formulation of our Helmholtz problem posed on the union of all interfaces. The corresponding operator takes the form "identity + non-expansive".

scholarly journals A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

2021 ◽  
Author(s):  
Chennakesava Kadapa
Keyword(s):  
Wave Propagation ◽  
Wave Speed ◽  
Critical Time ◽  
Incompressible Material ◽  
Implicit Scheme ◽  
Bulk Wave ◽  
Lumped Mass ◽  
Time Step ◽  
Material Models ◽  
Shear Wave Speed

AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

Speed of stress wave propagation in lung

1986 ◽  
Vol 61 (2) ◽  
pp. 701-705 ◽  
Author(s):  
R. T. Yen ◽  
Y. C. Fung ◽  
H. H. Ho ◽  
G. Butterman
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Impact Loading ◽  
Wave Speed ◽  
Dynamic Pressure ◽  
Transpulmonary Pressure ◽  
Lung Parenchyma ◽  
Surface Velocity ◽  
Stress Wave Propagation ◽  
Rabbit Lung

The speed of stress waves in the lung parenchyma was investigated to understand why, among all internal organs, the lung is the most easily injured when an animal is subjected to an impact loading. The speed of the sound is much less in the lung than that in other organs. To analyze the dynamic response of the lung to impact loading, it is necessary to know the speed of internal wave propagation. Excised lungs of the rabbit and the goat were impacted with water jet at dynamic pressure in the range of 7–35 kPa (1–5 psi) and surface velocity of 1–15 m/s. The stress wave was measured by pressure transducer. The distance between the point of impact and the sensor at another point on the far side of the lung and the transit time of the stress wave were measured. The wave speed in the goat lung was found to vary from 31.4 to 64.7 m/s when the transpulmonary pressure Pa-Ppl was varied from 0 to 20 cmH2O where Pa represents airway pressure and Ppl represents pleural pressure. In rabbit lung the wave speed varied from 16.5 to 36.9 m/s when Pa-Ppl was varied from 0 to 16 cmH2O. Using measured values of the bulk modulus, shear modulus, and density of the parenchyma, reasonable agreement between theoretical and experimental wave speeds were obtained.

scholarly journals Wave Propagation in Thin-Walled Aortic Analogues

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
C. G. Giannopapa ◽  
J. M. B. Kroot ◽  
A. S. Tijsseling ◽  
M. C. M. Rutten ◽  
F. N. van de Vosse
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Frequency Domain ◽  
Analytical Model ◽  
Viscoelastic Properties ◽  
Numerical Models ◽  
Computational Cost ◽  
One Dimensional ◽  
Arterial Blood

Research on wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flows. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one-dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models, well defined in vitro experiments are of great importance. The objective of this paper is to present a frequency domain analytical model based on the one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogs. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, volumetric flow rate, and wall distention obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

scholarly journals Wave Propagation Across Acoustic/Biot’s Media: A Finite-Difference Method

2013 ◽  
Vol 13 (4) ◽  
pp. 985-1012 ◽  
Author(s):  
Guillaume Chiavassa ◽  
Bruno Lombard
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressional Wave ◽  
Interface Conditions ◽  
Immersed Interface Method ◽  
Fluid Medium ◽  
Strang Splitting

AbstractNumerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-posedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time- marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.

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