A Sommerfeld non-reflecting boundary condition for the wave equation in mixed form

Espinoza, Hector; Codina, Ramon; Badia, Santiago

doi:10.1016/j.cma.2014.03.015

Cited by 31 publications

(39 citation statements)

References 41 publications

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“…The proofs are similar to the ones shown in [10,11], but considering now the time-discretization as well. Only one of such proofs will be developed here, the others following very similar strategies.…”

Section: Preliminariessupporting

confidence: 54%

“…We stress the fact that the convergence rates do depend on the choice of the stabilization parameters, and different convergence orders are obtained for the three discrete variational formulations above. Let us note that the time discretization schemes do not spoil the spatial convergence rates obtained in [10,11] for the timecontinuous case. Let us mention that the negative powers of h appear due to some terms in the error function having τ p or τ u dividing (see See Tables 4 and 5).…”

Section: Accuracy Of the Fully Discrete Methodsmentioning

confidence: 99%

“…In particular, we can consider equal interpolation for the unknowns. Stability and convergence of the stabilized FE spatial semidiscretization of the mixed wave equation has been presented in [10,11]. Stability and convergence of fully discrete schemes has also been analyzed for the convection-diffusion equation and the Stokes equations in [12,13,14] using spatial and temporal approximations related to those used in the present work.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical results are presented in Section 5 and, finally, in Section 6 the conclusions of the work are summarized. This paper is a continuation of our work on the approximation of the mixed form of the wave equation presented in [10,11]. Frequent reference is made to these two papers, to which the reader is addressed for details.…”

Section: Introductionmentioning

confidence: 99%

“…With regard to the space approximation, the Galerkin FE discretization of this mixed wave equation requires to satisfy a compatibility condition between the spaces of the two unknowns (scalar and vector), i.e., to use so-called inf-sup compatible interpolations. Alternatively, we can consider stabilized FE methods, which provide much more flexibility when choosing the interpolation spaces [9,10,11]. In particular, we can consider equal interpolation for the unknowns.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On some time marching schemes for the stabilized finite element approximation of the mixed wave equation

Espinoza

Codina

Badia

2015

Computer Methods in Applied Mechanics and Engineering

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In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is discretized in space using stabilized finite elements. On the one hand, stability and convergence analyses of the fully discrete numerical schemes are presented using different time integration schemes and appropriate functional settings. On the other hand, we use Fourier techniques (also known as von Neumann analysis) in order to analyze stability, dispersion and dissipation. Numerical convergence tests are presented for various time integration schemes, polynomial interpolations (for the spatial discretization), stabilization methods, and variational forms. To analyze the behavior of the different schemes considered, a 1D wave propagation problem is solved.

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Section: Preliminariessupporting

confidence: 54%

Section: Accuracy Of the Fully Discrete Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On some time marching schemes for the stabilized finite element approximation of the mixed wave equation

Espinoza

Codina

Badia

2015

Computer Methods in Applied Mechanics and Engineering

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Computational aeroacoustics to identify sound sources in the generation of sibilant /s/

Pont

Guasch

Baiges

et al. 2018

Numer Methods Biomed Eng

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A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between the upper and lower incisors and then impinges the space between the lower incisors and the lower lip. The flow eddies in that region become a source of direct aerodynamic sound, which is also diffracted by the speech articulators and radiated outwards. The numerical simulation of these phenomena is complex. The spectrum of an /s/ typically peaks between 4 and 10 kHz, which implies that very fine computational meshes are needed to capture the eddies producing such high frequencies. In this work, a large-scale computation of the aeroacoustics of /s/ has been performed for a realistic vocal tract geometry, resorting to two different acoustic analogies. A stabilized finite element method that acts as a large eddy simulation model has been adopted to solve the flow dynamics. Also, a numerical strategy has been implemented that allows the determination, in a single computational run, of the separate contribution of the sound diffracted by the upper incisors from the overall radiated sound. Results are presented for points located close to the lip opening showing the relative influence of the upper teeth depending on frequency.

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Reconstruction of vocal tract geometries from biomechanical simulations

Dabbaghchian

Arnela

Engwall

et al. 2018

Numer Methods Biomed Eng

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Medical imaging techniques are usually utilized to acquire the vocal tract geometry in 3D, which may then be used, eg, for acoustic/fluid simulation. As an alternative, such a geometry may also be acquired from a biomechanical simulation, which allows to alter the anatomy and/or articulation to study a variety of configurations. In a biomechanical model, each physical structure is described by its geometry and its properties (such as mass, stiffness, and muscles). In such a model, the vocal tract itself does not have an explicit representation, since it is a cavity rather than a physical structure. Instead, its geometry is defined implicitly by all the structures surrounding the cavity, and such an implicit representation may not be suitable for visualization or for acoustic/fluid simulation. In this work, we propose a method to reconstruct the vocal tract geometry at each time step during the biomechanical simulation. Complexity of the problem, which arises from model alignment artifacts, is addressed by the proposed method. In addition to the main cavity, other small cavities, including the piriform fossa, the sublingual cavity, and the interdental space, can be reconstructed. These cavities may appear or disappear by the position of the larynx, the mandible, and the tongue. To illustrate our method, various static and temporal geometries of the vocal tract are reconstructed and visualized. As a proof of concept, the reconstructed geometries of three cardinal vowels are further used in an acoustic simulation, and the corresponding transfer functions are derived.

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A Sommerfeld non-reflecting boundary condition for the wave equation in mixed form

Cited by 31 publications

References 41 publications

On some time marching schemes for the stabilized finite element approximation of the mixed wave equation

On some time marching schemes for the stabilized finite element approximation of the mixed wave equation

Computational aeroacoustics to identify sound sources in the generation of sibilant /s/

Reconstruction of vocal tract geometries from biomechanical simulations

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