scholarly journals Rayleigh–Bloch waves along elastic diffraction gratings

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140465 ◽  
Author(s):  
D. J. Colquitt ◽  
R. V. Craster ◽  
T. Antonakakis ◽  
S. Guenneau
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Elastic System ◽  
Diffraction Gratings ◽  
Effective Medium ◽  
Scalar Wave ◽  
Trapped Modes ◽  
Bloch Waves

Rayleigh–Bloch (RB) waves in elasticity, in contrast to those in scalar wave systems, appear to have had little attention. Despite the importance of RB waves in applications, their connections to trapped modes and the ubiquitous nature of diffraction gratings, there has been no investigation of whether such waves occur within elastic diffraction gratings for the in-plane vector elastic system. We identify boundary conditions that support such waves and numerical simulations confirm their presence. An asymptotic technique is also developed to generate effective medium homogenized equations for the grating that allows us to replace the detailed microstructure by a continuum representation. Further numerical simulations confirm that the asymptotic scheme captures the essential features of these waves.

Vibrational energy distribution in plate excited with random white noise

2021 ◽  
Vol 263 (6) ◽  
pp. 965-969
Author(s):  
Tyrode Victor ◽  
Nicolas Totaro ◽  
Laurent Maxit ◽  
Alain Le Bot
Keyword(s):  
Boundary Conditions ◽  
Energy Distribution ◽  
White Noise ◽  
Numerical Simulations ◽  
Ray Tracing ◽  
Energy Analysis ◽  
Vibrational Energy ◽  
Statistical Energy Analysis ◽  
Vibrational Energy Distribution ◽  
Tracing Method

In Statistical Energy Analysis (SEA) and more generally in all statistical theories of sound and vibration, the establishment of diffuse field in subsystems is one of the most important assumption. Diffuse field is a special state of vibration for which the vibrational energy is homogeneously and isotropically distributed. For subsystems excited with a random white noise, the vibration tends to become diffuse when the number of modes is large and the damping sufficiently light. However even under these conditions, the so-called coherent backscattering enhancement (CBE) observed for certain symmetric subsystems may impede diffusivity. In this study, CBE is observed numerically and experimentally for various geometries of subsystem. Also, it is shown that asymmetric boundary conditions leads to reduce or even vanish the CBE. Theoretical and numerical simulations with the ray tracing method are provided to support the discussion.

ON BOUNDARY CONDITIONS IN THE FINITE VOLUME LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES

1999 ◽  
Vol 10 (06) ◽  
pp. 1003-1016 ◽  
Author(s):  
GONGWEN PENG ◽  
HAOWEN XI ◽  
SO-HSIANG CHOU
Keyword(s):  
Shear Flow ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Simple Shear ◽  
Lattice Boltzmann ◽  
Unstructured Meshes ◽  
Simple Shear Flow ◽  
Boltzmann Method

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

Modelling of semiconductor rib wave guides by a finite difference method

1991 ◽  
Vol 69 (3-4) ◽  
pp. 512-519 ◽  
Author(s):  
A. Delâge
Keyword(s):  
Refractive Index ◽  
Boundary Conditions ◽  
Abrupt Change ◽  
Multiple Quantum Well ◽  
External Boundary ◽  
Multiple Quantum ◽  
Scalar Wave ◽  
Accurate Evaluation ◽  
Wave Guides ◽  
Mode Characteristics

The method of finite differences is used to solve the scalar wave equation for semiconductor rib wave guides. Boundary conditions derived from continuity relations are applied between regions of different refractive index, allowing more accurate evaluation of the propagation constants for ideal cases of abrupt change in the index. Also appropriate external boundary conditions alleviate the inaccuracy generally introduced by setting the field equal to zero on the external limit of the mesh. Our results agree with various other techniques when applied to typical guiding structures. As an example, we model a multiple-quantum-well structure by using an equivalent layered structure. Mode characteristics and confinement factors obtained by the method are of interest in understanding the behaviour of the lasers and modulators fabricated in our laboratory.

Experimental and numerical investigation of the transient characteristics and volute casing wall pressure fluctuations of a single-blade pump

2018 ◽  
Vol 233 (2) ◽  
pp. 280-291 ◽  
Author(s):  
Steffen Melzer ◽  
Tim Müller ◽  
Stephan Schepeler ◽  
Tobias Kalkkuhl ◽  
Romuald Skoda
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Pressure Amplitude ◽  
Centrifugal Pumps ◽  
Transient Pressure ◽  
Time Step ◽  
Wall Pressure Fluctuations

In contrast to conventional multiblade centrifugal pumps, single-blade pumps are characterized by a significant fluctuation of head and highly transient and circumferentially nonuniform flow field even in the best-efficiency point. For a contribution to a better understanding of the flow field and an improvement of numerical methods, a combined experimental and numerical study is performed with special emphasis on the analysis of the transient pressure field. In an open test rig, piezoresistive pressure sensors are utilized for the measurement of transient in- and outflow conditions and the volute casing wall pressure fluctuations. The quality of the numerical simulations is ensured by a careful adoption of the real geometry details in the simulation model, a grid study and a time step study. While the power curve is well reproduced by the numerical simulations, the time-averaged head is systematically overpredicted, probably due to underestimation of losses. Transient pressure boundary conditions for the numerical simulation show a better prediction of the measured pressure amplitude than constant boundary conditions, whereas the time-averaged head prediction is not improved. For a more accurate prediction of the transient flow field and the time-averaged characteristics, the utilization of scale-resolving turbulence models is assumed to be indispensable.

Numerical simulation of the Late Jurassic closure of the Vardar Tethys

2021 ◽  
Author(s):  
Nikola Stanković ◽  
Vesna Cvetkov ◽  
Vladica Cvetković
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Numerical Study ◽  
Phase Evolution ◽  
Staggered Grid ◽  
Second Phase ◽  
Weak Zone ◽  
Ongoing Research ◽  
Magmatic Complex

<p>We report updated results of our ongoing research on constraining geodynamic conditions associated with the final closure of the Vardar branch of the Tethys Ocean by means of application of numerical simulations (previous interim results reported in EGU2020-5919).</p><p>The aim of our numerical study is to test the hypothesis that a single eastward subduction in the Jurassic is a valid explanation for the occurrence of three major, presently observed geological entities that are left behind after the closure of the Vardar Tethys. These include: ophiolite-like igneous rocks of the Sava-Vardar zone and presumably subduction related Timok Magmatic Complex, both Late Cretaceous in age as well as Jurassic ophiolites obducted onto the Adriatic margin. In our simulations we initiate an intraoceanic subduction in the Early/Middle Jurassic, which eventually transitions into an oceanic closure and subsequent continental collision processes.</p><p>In the scope of our study numerical simulations are performed by solving a set of partial differential equations: the continuity equation, the Navier-Stokes equations and the temperature equation. To this end we used I2VIS thermo-mechanical code which utilizes marker in cell approach with finite difference discretization of equations on a staggered grid [Gerya et al., 2000; Gerya&Yuen, 2003].</p><p>The 2D model consists of two continental plates separated by two oceanic slabs connected at a mid-oceanic ridge. Intraoceanic subduction is initiated along the ridge by assigning a weak zone beneath the ridge. Time-dependent boundary conditions for velocity are imposed on the simulation in order to model a transient spreading period. The change of sign in plate velocities is found to be useful for both obtaining obduction / ophiolite emplacement [Duretz et al., 2016] and causing back-arc extension. Changes in velocities are linear in time. Simulations follow a three-phase evolution of velocity boundary conditions consisting of two convergent phases separated by a single divergent phase where spreading regime is dominant. Effect of duration and magnitude of the second phase on model evolution is also explored.</p><p>Our so far obtained simulations were able to reproduce the westward obduction and certain extension processes along the active (European) margin, which match the existing geological relationships. However, the simulations involve an unreasonably short geodynamic event (cca 15-20 My) and we are working on solving this problem with new simulations. </p>

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