Spurious Reflections Research Articles

Perfectly matched discrete layers for modeling unbounded domains

The method of perfectly matched layers (PML) is based on the elegant idea of introducing attenuation while keeping impedance unaltered, thus resulting in effective absorption of waves without spurious reflections. Due to its simplicity and effectiveness, PML has been widely used over the past 25 years to model wave propagation in unbounded domains. However, an acknowledged challenge is that PML no longer preserves impedance once the domain and the PML region are discretized, leading to spurious reflection at the interface. This issue has been fixed with the help of so-called impedance preserving discretization, leading to the method of perfectly matched discrete layers (PMDL), developed more than a decade ago. The idea is based on the observation that midpoint integration completely eliminates the discretization error in impedance that arises from linear finite element discretization. Beyond eliminating reflections at the interface, impedance preserving discretization is shown to be crucial to achieving stability of absorbing boundary conditions in situations with differing signs of phase and group velocities, e.g., anisotropic media. This talk will be an exposition of the development of the PMDL by the author and his collaborators, staring with fundamental ideas impedance preserving discretization followed by more advanced ABCs for anisotropic and periodic media.

One-dimensional moving window atomistic framework to model long-time shock wave propagation

We develop a long-time moving window framework using Molecular Dynamics (MD) to model shock wave propagation through a one-dimensional chain of atoms. The moving window formulation “follows” a propagating shock wave allowing us to model shock wave propagation much longer than conventional non-equilibrium MD (NEMD) simulations. This formulation also significantly decreases the required domain size and thus reduces the overall computational cost. The domain is divided into a purely atomistic “window” region containing the shock wave flanked by boundary or “continuum” regions on either end which incorporate continuum shock conditions. Spurious wave reflections are removed by employing a damping band method using the Langevin thermostat applied locally to the atoms in each continuum region. The moving window effect is achieved by adding/removing atoms to/from the window and boundary regions, and thus the shock wave front is focused at the center of the window region indefinitely. We simulate the shock through a one-dimensional chain of copper atoms using either the Lennard-Jones, modified Morse, or Embedded Atom Model (EAM) interatomic potential. We first perform verification studies to ensure proper implementation of the thermostat, potential functions, and damping band method, respectively. Next, we track the propagating shock and compare the actual shock velocity and average particle velocity to their corresponding analytical input values. From these comparisons, we optimize the linear shock Hugoniot relation for the given “lattice” orientation and compare these results to those in literature. When incorporated into the linear shock equation, these new Hugoniot parameters are shown to produce a stationary shock wave front. Finally, we perform one-dimensional moving window simulations of an unsteady, structured shock up to a few nanoseconds and characterize the increase in the shock front’s width.

A true PML approach for steady-state vibration analysis of an elastically supported beam under moving load by a DLSFEM formulation

This paper concerns a computational implementation for solving a Moving Load (ML) problem on an infinite Euler–Bernoulli elastic beam on a Pasternak visco-elastic support. A steady-state dynamic response in convected coordinate is sought, by a numerical approach with discretization over a finite domain, implying spurious boundary reflections of non-evanescent waves. This is effectively solved by: (a) analytically formulating a new, true Perfectly Matched Layer (PML) approach, toward handling the underlying fourth-order differential problem and the corresponding far-field conditions, without adopting special boundary conditions; (b) outlining a local Discontinuous Least-Squares Finite Element Method (DLSFEM) formulation, apt to provide a robust approach for the present non self-adjoint problem and to conveniently handle the jump condition in the shear force at the concentrated ML position. Consistent numerical results are illustrated and compared to an available analytical solution, showing a perfect match, with a complete removal of spurious boundary effects and a proof of theoretical a priori error estimates. Further results are produced for a case with multiple MLs. The paper shows that the present innovative DLSFEM-PML formulation is effectively suitable to numerically solve a steady-state ML problem on an infinite beam, setting up a new computational tool in such a challenging mechanical context.

An improved method for mean flow boundary conditions for computational aeroacoustics

An accelerated method of specifying Mean Flow Boundary Conditions for an unsteady flow is developed. Computation domains are inevitably finite in size, which means that its boundaries have to be located within the flow itself. This requires special boundary conditions which do not reflect outgoing waves while still being able to impose any incoming disturbances into the computation domain. As is well known, the Euler equations contain acoustic, vortical, and entropy waves, and all possible flows can be made by combining them. Because these waves are coupled, it is difficult to separate them into individual waves that the solver can modify. Moreover, it is desirable to set not just the waves but the mean of the combination of these waves at the boundaries and this takes a very long time. In this work, a new method for imposing the desired time-averaged mean flow at these computational boundaries is introduced. To reduce the complexity of the problem, but retaining the basic physics and difficulties, one-dimensional acoustic wave transmission is used to model wave propagation through a nearly choked nozzle. Mean and unsteady flow equations solved, simultaneously; and integrated with the existing non reflecting boundary conditions, and is able to quickly and accurately achieve the desired mean flow without spurious reflections of the outgoing disturbances, not only for deterministic, but chaotic flows.

Optimization of the POlarimeter-INTerferometer diagnostics system on EAST

A double-pass, radial-view, 11-chord POlarimeter-INTerferometer (POINT) system has been routinely operated on the Experimental Advanced Superconducting Tokamak (EAST) to provide electron density and current density information for physics research. Stray light occurs due to spurious reflections from optical elements, including lenses, waveplates, windows, and even detectors, along the optical path and can seriously deteriorate the accuracy of the Faraday rotation measurements. As a result of stray light contamination, periodic oscillations can be observed in the Faraday rotation data during the density ramp-up phase. Aiming to realize real-time current profile feedback control using Faraday effect measurements, the contamination from stray light must be removed. Some optimization methods have been explored to decrease the error induced by stray light. The results show that the Faraday angle oscillation during the density ramp-up phase is reduced from 3̂–5̂ to 0.5̂–1̂ (double-pass). Measurement of the noncollinearity error is also performed for the POINT system on EAST. This optimization allows for more accurate current profile measurements for physics research.

Pubertal timing and adolescent delinquency†

AbstractEarly pubertal timing (PT) increases the risk of adolescent delinquency, whereas late development reduces this risk; however, the mechanisms explaining PT effects on delinquency remain elusive. Theoretically, the PT–delinquency relationship is as a result of changes in parental supervision, peer affiliations, and body‐image perceptions or is a spurious reflection of early life risk factors. Using intergenerational data from the Millennium Cohort Study, a prospective sample of children followed from infancy to age 14 years in the United Kingdom (N = 11,556 parent–child pairs), we find that for both boys and girls, early PT is associated with heightened risks of delinquency, relative to on‐time puberty, whereas late PT is associated with lower risks, even after controlling for a large share of childhood confounders. Mediation test results indicate that changes in parental supervision, peer affiliations, and body‐image perceptions from ages 11 to 14 partly account for associations between off‐time PT and delinquency. Our findings are most consistent with criminological theories in which the psychosocial, familial, and peer group changes that accompany off‐time pubertal development are emphasized. Changes in peer substance use, in particular, were the primary explanatory factor for the relationships between early and late PT and delinquency, for both boys and girls.

Direct computation of aeroacoustic fields in laminar flows: Solver development and assessment of wall temperature effects on radiated sound around bluff bodies

This work presents results of a direct computation of acoustic fields produced by several laminar flow configurations. A solver specifically developed for compressible mass, momentum and energy equations, named caafoam, is presented. Low–storage high-order Runge-Kutta schemes were used for time integration, and an unstructured colocated finite–volume method for space discretization. A sponge-layer-type non-reflective boundary treatment was adopted to avoid spurious numerical reflections at the far-field boundaries. These techniques were chosen and tested to see if they enable a broad range of physical phenomena, with a particular emphasis on aeroacoustic problems, to be solved. The reliability, efficiency and robustness of caafoam was demonstrated by computing several benchmarks concerning far-field aerodynamic sound. After proving the direct simulation capabilities of caafoam, it was used to analyze the effect of the wall temperature conditions on the aeroacoustic sound produced by laminar flows over bluff bodies.

Broadband electrically tunable VO2‑Metamaterial terahertz switch with suppressed reflection

AbstractDevices designed to dynamically control the transmission, reflection, and absorption of terahertz (THz) radiation are essential for the development of a broad range of THz technologies. A viable approach utilizes materials which undergo an insulator‐to‐metal transition (IMT), switching from transmissive to reflective upon becoming metallic. However, for many applications, it is undesirable to have spurious reflections that can scatter incident light and induce noise to the system. We present an electrically actuated, broadband THz switch which transitions from a transparent state with low reflectivity, to an absorptive state for which both the reflectivity and transmission are strongly suppressed. Our device consists of a patterned high‐resistivity silicon metamaterial layer that provides broadband reflection suppression by matching the impedance of free space. This is integrated with a VO2 ground plane, which undergoes an IMT by means of a DC bias applied to an interdigitated electrode. THz time domain spectroscopy measurements reveal an active bandwidth of 700 GHz with suppressed reflection and more than 90% transmission amplitude modulation with a low insertion loss. We utilize finite‐difference time domain (FDTD) simulations in order to examine the loss mechanisms of the device, as well as the sensitivity to polarization and incident angle. This device validates a general approach toward suppressing unwanted reflections in THz modulators and switches which can be easily adapted to a broad array of applications through straightforward modifications of the structural parameters.

Strong compact formalism for characteristic boundary conditions with discontinuous spectral methods

Characteristic boundary conditions for the Navier-Stokes equations (NSCBC) are implemented for the first time with discontinuous spectral methods, namely the spectral difference and flux reconstruction. The implementation makes use of the resolution by these methods of the strong form of the Navier-Stokes equations by applying these conditions through a flux balance regularization which takes the form of a generalized element-compact correction polynomial. It is shown to be at least as effective as similar implementations in finite volume solvers, and sustains arbitrarily-high orders of accuracy on hexahedral-based unstructured meshes. Further, Navier-Stokes time-domain impedance boundary conditions are derived and implemented as a NSCBC sub-class. They account for the diffusive process at the wall and are shown to properly resolve the broadband response of porous materials under normal and grazing flow conditions. The ability of these NSCBC in preventing the appearance of spurious reflections at the boundaries is demonstrated through a varied series of bench-marking simulations. They effectively shield the inner computational domain from any far-field unphysical contamination. Overall, this work enables the use of strong discontinuous spectral methods to study unsteady problems on complex geometries.

A local grid refinement scheme for B‐spline material point method

SummaryA local grid refinement scheme for the material point method with B‐spline basis functions (BSMPM) is developed based on the concept of bridging domain approach. The fine grid is defined in the local large‐deformation regions to accurately capture the complex material responses, whereas other spatial domains are discritized by coarse grids. In the overlapping domain between the fine and coarse grids, the constraint of particle displacements obtained with different grids is enforced using the Lagrange multiplier method to eliminate the spurious stress reflection at the fine/coarse grid interface. Representative numerical examples have shown that the BSMPM simulations with the proposed local grid refinement scheme could provide the solutions in good agreement with those obtained with the uniformly fine grid, and that no significant spurious stress reflection is induced at the fine/coarse grid interface, even for the bridging domain size as small as the cell size of the fine grid. It is also found that the proposed local grid refinement method can significantly reduce the BSMPM computational time compared with the cases for uniformly fine grids. A multitime‐step algorithm is presented and shown to considerably enhance the efficiency of the present local grid refinement scheme with no compromise in accuracy.

FINITE ELEMENT SOLUTION OF WAVE EQUATION WITH REDUCTION OF THE VELOCITY DISPERSION AND SPURIOUS REFLECTION

ABSTRACT The objective of this paper is to present a finite element solution for the wave propagation problems with a reduction of the velocity dispersion and spurious reflection. To this end, a high-order two-step direct integration algorithm for the wave equation is adopted. The suggested algorithm is formulated in terms of two Hermitian finite difference operators with a sixth-order local truncation error in time. The two-node linear finite element presenting the fourth-order of local truncation error is considered. The numerical results reveal that although the algorithm competes with higher-order algorithms presented in the literature, the computational effort required is similar to the effort required by the average acceleration Newmark method. More than that, the integration with the lumped mass model shows similar results to the integration using the average acceleration Newmark for the consistent mass model, which involves a higher number of computational operations.

Measuring the Acoustic Characteristics of a Helicopter Rotormodel in a Wind Tunnel

The article presents the results of comparative experimental and computational studies of the acoustic characteristics of the model of a helicopter rotor performed in the modernized test section of the T-1K wind tunnel (WT). In order to identify and minimize the influence of spurious reflections on the studied acoustic characteristics using the Maximum Length Sequence method (M-sequence method) in the T-1K WT, we analyzed the microphone arrangement, which showed that the largest spurious contribution to the measured signal comes from reflections from the WT T-1K wall located behind the microphones. Comparison of the experimentally measured noise levels with the wall raised and lowered confirmed that the wall influences the measured acoustic noise characteristics of the model rotor. Comparison of experimental data with numerical simulation results allowed the conclusion that the WT T-1K modernized wind tunnel is fundamentally suitable to validate numerical methods of calculating the aeroacoustic characteristics of model rotors.

Partition of Unity Finite Element Method applied to exterior problems with Perfectly Matched Layers

The Partition of Unity Finite Element Method (PUFEM) is now a well established and efficient method used in computational acoustics to tackle short-wave problems. This method is an extension of the classical finite element method whereby enrichment functions are used in the approximation basis in order to enhance the convergence of the method whilst maintaining a relatively low number of degrees of freedom. For exterior problems, the computational domain must be artificially truncated and special treatments must be followed in order to avoid or reduce spurious reflections. In recent papers, different Non-Reflecting Boundary Conditions (NRBCs) have been used in conjunction with the PUFEM. An alternative is to use the Perfectly Match Layer (PML) concept which consists in adding a computational sponge layer which prevents reflections from the boundary. In contrast with other NRBCs, the PML is not case specific and can be applied to a variety of configurations. The aim of this work is to show the applicability of PML combined with PUFEM for solving the propagation of acoustic waves in unbounded media. Performances of the PUFEM-PML are shown for different configurations ranging from guided waves in ducts, radiation in free space and half-space problems. In all cases, the method is shown to provide acceptable results for most applications, similar to that of local approximation of NRBCs.

Efficient stability analysis of fluid flows using complex mapping techniques

Global linear stability analysis of open flows leads to difficulties associated to boundary conditions, leading to either spurious wave reflections (in compressible cases) or to non-local feedback due to the elliptic nature of the pressure equation (in incompressible cases). A novel approach is introduced to address both these problems. The approach consists of solving the problem using a complex mapping of the spatial coordinates, in a way that can be directly applicable in an existing code without any additional auxiliary variable. The efficiency of the method is first demonstrated for a simple 1D equation modeling incompressible Navier–Stokes, and for a linear acoustics problem. The application to full linearized Navier–Stokes equation is then discussed. A criterion on how to select the parameters of the mapping function is derived by analyzing the effect of the mapping on plane wave solutions. Finally, the method is demonstrated for three application cases, including an incompressible jet, a compressible hole-tone configuration and the flow past an airfoil. The examples allow to show that the method allows to suppress the artificial modes which otherwise dominate the spectrum and can possibly hide the physical modes. Finally, it is shown that the method is still efficient for small truncated domains, even in cases where the computational domain is comparable to the dominant wavelength.

Stretching, Amplification, and Compression of Microwave Pulses Using Helically Corrugated Waveguides

We demonstrate the possible implementation of the chirped pulse amplification (CPA) method, which is widely used in optics, for the microwave frequency band. This method is based on the preliminary elongation of the incident pulse in the stretcher, sequential amplification of spectral components in a wideband amplifier, and final compression in a line with negative dispersion (compressor). A circuit is considered in which multifold, helically corrugated waveguides are used as an operating space in each section, including a stretcher, an amplifier, and a compressor. The dispersion characteristics of such waveguides can vary significantly when its geometrical parameters are changed, which makes it possible to ensure optimal dispersion characteristics in the stretcher and compressor, as well as the largest gain bandwidth in the amplifier. In addition, these dispersive elements allow us to avoid spurious reflection of the signal due to the absence of a stopband in the operating frequency range. Simulations within the framework of the coupledwave approach showed the prospects of the circuit proposed. In particular, using an experimentally realized 30-GHz gyro-TWT, the peak power of a 200-ns, 300-W incident pulse can be increased up to 4 MW, which is about six times higher than the power of the driving electron beam. With direct amplification (in the absence of a stretcher and a compressor) of the specified incident pulse in the same gyro-TWT, the output peak power does not exceed 250 kW.

A generating and absorbing boundary condition for dispersive waves in detailed simulations of free-surface flow interaction with marine structures

The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh, in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.

A fractional step method for computational aeroacoustics using weak imposition of Dirichlet boundary conditions

In this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow scales at once. After space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to weakly impose Dirichlet boundary conditions via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.

Toward a Feedback-Insensitive Semiconductor Laser

We present a route toward design and fabrication of a conceptually new type of optical feedback insensitive integrated semiconductor ring laser with a weak optical isolator included in the ring. Although the approach has not resulted in the clear advantages that were aimed at, this detailed account of the process we believe is valuable to readers active in the field. After a summary of optical-feedback sensitivity in semiconductor lasers, we review various attempts toward reducing this sensitivity and discuss the feasibility of the concept of weak intra-cavity isolation. The design, model and theory of the novel integrated ring laser device are presented. The observed 5 dB of isolation and 3 dB increase of tolerance for external optical feedback demonstrate the feasibility of the intra-cavity isolation concept. However, the observed output performance of the single-mode laser, both with and without activated intra-cavity isolation, suggests the presence of a spurious intra-cavity reflection, strongly coupling the directional modes. Due to this coupling, the sensitivity to external optical feedback is comparable to that of a Fabry–Perot type laser. Therefore, an alternate route is indicated toward a less complex laser cavity with potentially less intra-cavity reflection and better tolerance for external optical feedback.

Comparison of seismic interferometry techniques for the retrieval of seismic body waves in CO2 sequestration monitoring

AbstractAmbient noise seismic interferometry performed by cross-correlation has been proven to be a potential cost-effective technique for geological studies. To improve the resolution of images created by interferometry, additional techniques using deconvolution and cross-coherence have been introduced. While all three methods have previously been evaluated using surface wave data for shear-wave imaging of the near surface, comparatively little study has been devoted to assess the three methods for the retrieval of body waves in reflection surveys for time-lapse application. Moreover, although the application of seismic interferometry to CO2 sequestration by cross-correlation has been investigated by many researchers, to our knowledge, similar time-lapse studies have not been conducted using deconvolution and cross-coherence methods. We evaluate the three methods of cross-correlation, deconvolution and cross-coherence for the retrieval of phase information contained in virtual seismic records by applying seismic interferometry to synthetic data, using a model reservoir before and after CO2 injection. By examining two approaches of regularization and smoothing factors to suppress spurious reflection events observed on the deconvolution and cross-coherence results, we note that both approaches provide similar results. We investigate noise effects by adding random noise independently at each geophone. Finally, we apply these techniques to field data recorded near the CO2 storage site in Ketzin, Germany. For both our numerical and field data studies, we find that the cross-coherence technique retrieves the phase information of body-wave data more effectively than the cross-correlation and deconvolution techniques, and is less sensitive to uncorrelated noise from shallow sources.

Perfectly matched layer boundary conditions for the second‐order acoustic wave equation solved by the rapid expansion method

ABSTRACTWe derive a governing second‐order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite‐difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme, numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections from the model boundaries.